PODMAS 2

 

Intermediate Level Training:

Question 11:

Simplify:
$(10 + 5) \times (8 - 3) \div 5$

Solution:

1. Follow PODMAS: Parentheses first, then multiplication and division.
2. Step 1: Solve inside the parentheses:
   • $10 + 5 = 15$
   • $8 - 3 = 5$
3. Step 2: Multiply:
   $15 \times 5 = 75$
4. Step 3: Now, divide:
   $75 \div 5 = 15$

Answer: $15$

---

Question 12:

Simplify:
$9 \times (2^3 - 4) + 6$

Solution:

1. Follow PODMAS: Exponent first, then solve inside the parentheses, followed by multiplication and addition.
2. Step 1: Solve the exponent:
   $2^3 = 8$
3. Step 2: Solve inside the parentheses:
   $8 - 4 = 4$
4. Step 3: Multiply:
   $9 \times 4 = 36$
5. Step 4: Add:
   $36 + 6 = 42$

Answer: $42$

---

Question 13:

Simplify:
$16 \div (4 + 2) \times 3^2$

Solution:

1. Follow PODMAS: Solve the parentheses, then division, exponent, and multiplication.
2. Step 1: Solve inside the parentheses:
   $4 + 2 = 6$
3. Step 2: Solve the exponent:
   $3^2 = 9$
4. Step 3: Divide:
   $16 \div 6 = 2.67$ (rounded to two decimal places)
5. Step 4: Multiply:
   $2.67 \times 9 = 24$

Answer: $24$ (approximately)

---

Question 14:

Simplify:
$(5^2 - 7) + 4 \div (9 - 6)$

Solution:

1. Follow PODMAS: Exponent first, then parentheses, division, and addition.
2. Step 1: Solve the exponent:
   $5^2 = 25$
3. Step 2: Solve inside the parentheses:
   $9 - 6 = 3$
4. Step 3: Perform the division:
   $4 \div 3 = 1.33$ (rounded to two decimal places)
5. Step 4: Now, subtract and add:
   $25 - 7 = 18$, then $18 + 1.33 = 19.33$

Answer: $19.33$ (approximately)

---

Question 15:

Simplify:
$3^3 + (24 \div 8) \times (6 + 2)$

Solution:

1. Follow PODMAS: Exponent first, then parentheses, division, multiplication, and addition.
2. Step 1: Solve the exponent:
   $3^3 = 27$
3. Step 2: Solve inside the parentheses:
   • $24 \div 8 = 3$
   • $6 + 2 = 8$
4. Step 3: Multiply:
   $3 \times 8 = 24$
5. Step 4: Add:
   $27 + 24 = 51$

Answer: $51$

---

Question 16:

Simplify:
$(20 - 4^2) \div 2 + 7$

Solution:

1. Follow PODMAS: Exponent first, then solve inside the parentheses, perform division, and finally addition.
2. Step 1: Solve the exponent:
   $4^2 = 16$
3. Step 2: Solve inside the parentheses:
   $20 - 16 = 4$
4. Step 3: Perform the division:
   $4 \div 2 = 2$
5. Step 4: Now, add:
   $2 + 7 = 9$

Answer: $9$

---

Question 17:

Simplify:
$(6 \times 3) + 2^4 \div (4 - 2)$

Solution:

1. Follow PODMAS: Parentheses first, then exponent, multiplication, division, and addition.
2. Step 1: Solve inside the parentheses:
   $4 - 2 = 2$
3. Step 2: Solve the exponent:
   $2^4 = 16$
4. Step 3: Multiply:
   $6 \times 3 = 18$
5. Step 4: Perform the division:
   $16 \div 2 = 8$
6. Step 5: Add:
   $18 + 8 = 26$

Answer: $26$

---

Question 18:

Simplify:
$5 \times 2^3 + (15 \div 3) - 9$

Solution:

1. Follow PODMAS: Exponent first, then solve inside the parentheses, multiplication, division, and finally addition/subtraction.
2. Step 1: Solve the exponent:
   $2^3 = 8$
3. Step 2: Solve inside the parentheses:
   $15 \div 3 = 5$
4. Step 3: Perform the multiplication:
   $5 \times 8 = 40$
5. Step 4: Add and subtract from left to right:
   $40 + 5 = 45$, then $45 - 9 = 36$

Answer: $36$

---

Question 19:

Simplify:
$12 \div (3 + 9) \times (5 - 2)^2$

Solution:

1. Follow PODMAS: Parentheses first, then exponent, division, and multiplication.
2. Step 1: Solve inside the parentheses:
   • $3 + 9 = 12$
   • $5 - 2 = 3$
3. Step 2: Solve the exponent:
   $3^2 = 9$
4. Step 3: Perform the division:
   $12 \div 12 = 1$
5. Step 4: Multiply:
   $1 \times 9 = 9$

Answer: $9$

---

Question 20:

Simplify:
$7 + 4 \times (6^2 \div 9) - 3$

Solution:

1. Follow PODMAS: Exponent first, then solve inside the parentheses, perform multiplication/division, and finally addition/subtraction.
2. Step 1: Solve the exponent:
   $6^2 = 36$
3. Step 2: Perform the division inside the parentheses:
   $36 \div 9 = 4$
4. Step 3: Multiply:
   $4 \times 4 = 16$
5. Step 4: Add and subtract:
   $7 + 16 = 23$, then $23 - 3 = 20$

Answer: $20$

---

These problems require combining multiple steps in the right order and practicing the correct application of PODMAS (BODMAS). Let me know when you're ready for more intermediate-level questions or if you have any doubts!

Let’s move on to the advanced level. These problems will involve more complex operations, including multiple parentheses, exponents, and a combination of different operations. I will provide detailed explanations for each question.

---

Advanced Level Training:

Question 1:

Simplify:
$2 \times (3^2 + 4) - (8 \div 2) + 5^2$

Solution:

1. Follow PODMAS: Start with exponents, then parentheses, division, multiplication, and finally addition/subtraction.
2. Step 1: Solve the exponents:
   $3^2 = 9$ and $5^2 = 25$
3. Step 2: Solve inside the parentheses:
   $9 + 4 = 13$
4. Step 3: Perform the division:
   $8 \div 2 = 4$
5. Step 4: Multiply:
   $2 \times 13 = 26$
6. Step 5: Combine all parts:
   $26 - 4 + 25 = 47$

Answer: $47$

---

Question 2:

Simplify:
$(5^2 - 3) \times (4 + 6 \div 2)$

Solution:

1. Follow PODMAS: Handle exponents, then division, parentheses, and multiplication.
2. Step 1: Solve the exponent:
   $5^2 = 25$
3. Step 2: Solve inside the parentheses:
   $4 + 6 \div 2 = 4 + 3 = 7$
4. Step 3: Combine:
   $25 - 3 = 22$
5. Step 4: Multiply:
   $22 \times 7 = 154$

Answer: $154$

---

Question 3:

Simplify:
$(3 + 5) \times 2^3 - (4 \div 2)$

Solution:

1. Follow PODMAS: Solve inside the parentheses, then exponent, division, and finally multiplication.
2. Step 1: Solve inside the parentheses:
   $3 + 5 = 8$
3. Step 2: Solve the exponent:
   $2^3 = 8$
4. Step 3: Perform the division:
   $4 \div 2 = 2$
5. Step 4: Multiply:
   $8 \times 8 = 64$
6. Step 5: Combine:
   $64 - 2 = 62$

Answer: $62$

---

Question 4:

Simplify:
$2 \times (3 + 4^2) - 5^2 + (6 \div 3)$

Solution:

1. Follow PODMAS: Handle exponents, then parentheses, division, multiplication, and finally addition/subtraction.
2. Step 1: Solve the exponents:
   $4^2 = 16$ and $5^2 = 25$
3. Step 2: Solve inside the parentheses:
   $3 + 16 = 19$
4. Step 3: Perform the division:
   $6 \div 3 = 2$
5. Step 4: Multiply:
   $2 \times 19 = 38$
6. Step 5: Combine:
   $38 - 25 + 2 = 15$

Answer: $15$

---

Question 5:

Simplify:
$10 - (3 \times (4 + 2)) + 5^2 - 6^2$

Solution:

1. Follow PODMAS: Solve inside the parentheses, then multiplication, exponents, and finally addition/subtraction.
2. Step 1: Solve inside the parentheses:
   $4 + 2 = 6$
3. Step 2: Multiply:
   $3 \times 6 = 18$
4. Step 3: Solve the exponents:
   $5^2 = 25$ and $6^2 = 36$
5. Step 4: Combine:
   $10 - 18 + 25 - 36 = -19$

Answer: $-19$

---

Question 6:

Simplify:
$(2^4 + 3) \div (3 - 1) + (4 \times 3)$

Solution:

1. Follow PODMAS: Handle exponents, then parentheses, division, and multiplication.
2. Step 1: Solve the exponent:
   $2^4 = 16$
3. Step 2: Solve inside the parentheses:
   $3 - 1 = 2$ and $4 \times 3 = 12$
4. Step 3: Combine:
   $16 + 3 = 19$
5. Step 4: Perform the division:
   $19 \div 2 = 9.5$
6. Step 5: Combine:
   $9.5 + 12 = 21.5$

Answer: $21.5$

---

Question 7:

Simplify:
$5 + 2 \times (3^2 - 1) \div (4 - 2)$

Solution:

1. Follow PODMAS: Handle exponents, then parentheses, multiplication, division, and finally addition.
2. Step 1: Solve the exponent:
   $3^2 = 9$
3. Step 2: Solve inside the parentheses:
   $9 - 1 = 8$ and $4 - 2 = 2$
4. Step 3: Multiply:
   $2 \times 8 = 16$
5. Step 4: Perform the division:
   $16 \div 2 = 8$
6. Step 5: Combine:
   $5 + 8 = 13$

Answer: $13$

---

Question 8:

Simplify:
$(7 + 3) \times (5^2 - 2^3) \div 4$

Solution:

1. Follow PODMAS: Solve inside the parentheses and exponents, then multiplication, and finally division.
2. Step 1: Solve inside the parentheses:
   $7 + 3 = 10$
3. Step 2: Solve the exponents:
   $5^2 = 25$ and $2^3 = 8$
4. Step 3: Combine:
   $25 - 8 = 17$
5. Step 4: Multiply:
   $10 \times 17 = 170$
6. Step 5: Perform the division:
   $170 \div 4 = 42.5$

Answer: $42.5$

---

Question 9:

Simplify:
$3 \times (4 + 5) - (2^3 + 6) \div 2$

Solution:

1. Follow PODMAS: Solve inside the parentheses, then exponent, division, multiplication, and finally addition/subtraction.
2. Step 1: Solve inside the parentheses:
   $4 + 5 = 9$
3. Step 2: Solve the exponent:
   $2^3 = 8$
4. Step 3: Combine inside the parentheses:
   $8 + 6 = 14$
5. Step 4: Multiply:
   $3 \times 9 = 27$
6. Step 5: Perform the division:
   $14 \div 2 = 7$
7. Step 6: Combine:
   $27 - 7 = 20$

Answer: $20$

---

Question 10:

Simplify:
$(2 + 3^2) \times (4 - 1)^2 \div (5 - 3)$

Solution:

1. Follow PODMAS: Solve the exponents, then parentheses, division, and multiplication.
2. Step 1: Solve the exponents:
   $3^2 = 9$ and $(4 - 1)^2 = 3^2 = 9$
3. Step 2: Solve inside the parentheses:
   $2 + 9 = 11$
4. **Step

You said:

Continue

ChatGPT said:

Continuing from the last solution, let’s finish the calculations for Question 10 and then move on to more advanced level questions.

---

Question 10 (Continued):

Simplify:
$(2 + 3^2) \times (4 - 1)^2 \div (5 - 3)$

Solution (Continued):

1. Step 3 (continued): Solve inside the parentheses:
   • $(5 - 3) = 2$
2. Step 4: We previously found:
   • $2 + 9 = 11$
   • $(4 - 1)^2 = 3^2 = 9$
3. Step 5: Now, multiply:
   $11 \times 9 = 99$
4. Step 6: Finally, divide:
   $99 \div 2 = 49.5$

Answer: $49.5$

---

Advanced Level Training (Continued):

Question 11:

Simplify:
$(6 + 2) \times (3^2 - 4) - 5^2 + 7 \div (1 + 1)$

Solution:

1. Step 1: Solve the exponent:
   $3^2 = 9$
2. Step 2: Solve inside the parentheses:
   • $6 + 2 = 8$
   • $9 - 4 = 5$
3. Step 3: Multiply:
   $8 \times 5 = 40$
4. Step 4: Solve the exponent:
   $5^2 = 25$
5. Step 5: Solve inside the parentheses:
   $1 + 1 = 2$
6. Step 6: Perform the division:
   $7 \div 2 = 3.5$
7. Step 7: Combine all parts:
   $40 - 25 + 3.5 = 18.5$

Answer: $18.5$

---

Question 12:

Simplify:
$4 \times (5 - 2^2) + (8 \div 4) \times 3$

Solution:

1. Step 1: Solve the exponent:
   $2^2 = 4$
2. Step 2: Solve inside the parentheses:
   $5 - 4 = 1$
3. Step 3: Multiply:
   $4 \times 1 = 4$
4. Step 4: Solve the division:
   $8 \div 4 = 2$
5. Step 5: Multiply:
   $2 \times 3 = 6$
6. Step 6: Combine:
   $4 + 6 = 10$

Answer: $10$

---

Question 13:

Simplify:
$(3 + 5) \div 4 + 2 \times (5 - 1)$

Solution:

1. Step 1: Solve inside the parentheses:
   $3 + 5 = 8$ and $5 - 1 = 4$
2. Step 2: Perform the division:
   $8 \div 4 = 2$
3. Step 3: Multiply:
   $2 \times 4 = 8$
4. Step 4: Combine:
   $2 + 8 = 10$

Answer: $10$

---

Question 14:

Simplify:
$3 \times (2 + 4) - (7 - 3) \times 2$

Solution:

1. Step 1: Solve inside the parentheses:
   $2 + 4 = 6$ and $7 - 3 = 4$
2. Step 2: Multiply:
   $3 \times 6 = 18$ and $4 \times 2 = 8$
3. Step 3: Combine:
   $18 - 8 = 10$

Answer: $10$

---

Question 15:

Simplify:
$2 \times (3^3 - 4) + (5 \div 5)^2$

Solution:

1. Step 1: Solve the exponent:
   $3^3 = 27$
2. Step 2: Solve inside the parentheses:
   $27 - 4 = 23$
3. Step 3: Multiply:
   $2 \times 23 = 46$
4. Step 4: Solve the division and exponent:
   $5 \div 5 = 1$ and $1^2 = 1$
5. Step 5: Combine:
   $46 + 1 = 47$

Answer: $47$

---

Question 16:

Simplify:
$(6^2 - 4 \times 3) \div 2 + 5^2$

Solution:

1. Step 1: Solve the exponents:
   $6^2 = 36$ and $5^2 = 25$
2. Step 2: Multiply:
   $4 \times 3 = 12$
3. Step 3: Solve inside the parentheses:
   $36 - 12 = 24$
4. Step 4: Perform the division:
   $24 \div 2 = 12$
5. Step 5: Combine:
   $12 + 25 = 37$

Answer: $37$

---

Question 17:

Simplify:
$8 \div (2 + 2) \times (5 - 1)^2$

Solution:

1. Step 1: Solve inside the parentheses:
   $2 + 2 = 4$ and $5 - 1 = 4$
2. Step 2: Solve the exponent:
   $4^2 = 16$
3. Step 3: Perform the division:
   $8 \div 4 = 2$
4. Step 4: Multiply:
   $2 \times 16 = 32$

Answer: $32$

---

Question 18:

Simplify:
$(7 + 3) \times 2 - (2^3 + 4) \div 2$

Solution:

1. Step 1: Solve inside the parentheses:
   $7 + 3 = 10$
2. Step 2: Solve the exponent:
   $2^3 = 8$
3. Step 3: Combine inside the parentheses:
   $8 + 4 = 12$
4. Step 4: Multiply:
   $10 \times 2 = 20$
5. Step 5: Perform the division:
   $12 \div 2 = 6$
6. Step 6: Combine:
   $20 - 6 = 14$

Answer: $14$

---

Question 19:

Simplify:
$(5 \times 3^2) - (4 + 1)^2 + (8 \div 2)$

Solution:

1. Step 1: Solve the exponent:
   $3^2 = 9$ and $(4 + 1)^2 = 5^2 = 25$
2. Step 2: Multiply:
   $5 \times 9 = 45$
3. Step 3: Solve the division:
   $8 \div 2 = 4$
4. Step 4: Combine:
   $45 - 25 + 4 = 24$

Answer: $24$

---

Question 20:

Simplify:
$(10 - 2) \div (4 + 4 \div 2) + 5^2 - 3$

Solution:

1. Step 1: Solve the division:
   $4 \div 2 = 2$
2. Step 2: Solve inside the parentheses:
   $4 + 2 = 6$ and $10 - 2 = 8$
3. Step 3: Perform the division:
   $8 \div 6 = \frac{4}{3}$ or approximately $1.33$
4. . Step 3 (continued): Perform the division:

5.  4. Step 3 (continued): Perform the division:
   $8 \div 6 = \frac{4}{3}$ or approximately $1.33$ 5. Step 4: Solve the exponent:
   $5^2 = 25$ 6. Step 5: Combine everything:
   $1.33 + 25 - 3 = 23.33$

   Answer: $23.33$

Advanced Level (Next Set)

Question 21:

Simplify:
$(6 + 2^3) \times (5 - 3) \div 2$

Solution:

1. Step 1: Solve the exponent:
   $2^3 = 8$
2. Step 2: Solve inside the parentheses:
   $6 + 8 = 14$ and $5 - 3 = 2$
3. Step 3: Multiply:
   $14 \times 2 = 28$
4. Step 4: Perform the division:
   $28 \div 2 = 14$

Answer: $14$

---

Question 22:

Simplify:
$(4 \times 3^2) - (2^2 + 6 \div 3)$

Solution:

1. Step 1: Solve the exponent:
   $3^2 = 9$ and $2^2 = 4$
2. Step 2: Perform the division:
   $6 \div 3 = 2$
3. Step 3: Combine inside the parentheses:
   $4 + 2 = 6$
4. Step 4: Multiply:
   $4 \times 9 = 36$
5. Step 5: Combine:
   $36 - 6 = 30$

Answer: $30$

---

Question 23:

Simplify:
$5 + (6 \div 2)^2 - (3 \times 4)$

Solution:

1. Step 1: Perform the division:
   $6 \div 2 = 3$
2. Step 2: Solve the exponent:
   $3^2 = 9$
3. Step 3: Multiply:
   $3 \times 4 = 12$
4. Step 4: Combine:
   $5 + 9 - 12 = 2$

Answer: $2$

---

Question 24:

Simplify:
$10 \div (3 + 2^2) + 5 \times (4 - 1)$

Solution:

1. Step 1: Solve the exponent:
   $2^2 = 4$
2. Step 2: Solve inside the parentheses:
   $3 + 4 = 7$ and $4 - 1 = 3$
3. Step 3: Perform the division:
   $10 \div 7 \approx 1.43$
4. Step 4: Multiply:
   $5 \times 3 = 15$
5. Step 5: Combine:
   $1.43 + 15 = 16.43$

Answer: $16.43$

---

Question 25:

Simplify:
$(4 \times 3^2 - 2^4) \div (8 \div 2)$

Solution:

1. Step 1: Solve the exponents:
   $3^2 = 9$ and $2^4 = 16$
2. Step 2: Multiply:
   $4 \times 9 = 36$
3. Step 3: Combine inside the parentheses:
   $36 - 16 = 20$
4. Step 4: Perform the division:
   $8 \div 2 = 4$
5. Step 5: Combine:
   $20 \div 4 = 5$

Answer: $5$

---

Question 26:

Simplify:
$(7 + 3 \times 2^3) - (4 \div 2 + 5)$

Solution:

1. Step 1: Solve the exponent:
   $2^3 = 8$
2. Step 2: Multiply:
   $3 \times 8 = 24$
3. Step 3: Solve inside the parentheses:
   $7 + 24 = 31$ and $4 \div 2 = 2$
4. Step 4: Combine:
   $2 + 5 = 7$
5. Step 5: Final combine:
   $31 - 7 = 24$

Answer: $24$

---

Question 27:

Simplify:
$2^5 - (4 \times 3) + (6^2 \div 3)$

Solution:

1. Step 1: Solve the exponents:
   $2^5 = 32$ and $6^2 = 36$
2. Step 2: Multiply:
   $4 \times 3 = 12$
3. Step 3: Perform the division:
   $36 \div 3 = 12$
4. Step 4: Combine:
   $32 - 12 + 12 = 32$

Answer: $32$

---

Question 28:

Simplify:
$(5 + 3^2) \times 2 - (4^2 \div 2)$

Solution:

1. Step 1: Solve the exponents:
   $3^2 = 9$ and $4^2 = 16$
2. Step 2: Solve inside the parentheses:
   $5 + 9 = 14$
3. Step 3: Multiply:
   $14 \times 2 = 28$
4. Step 4: Perform the division:
   $16 \div 2 = 8$
5. Step 5: Combine:
   $28 - 8 = 20$

Answer: $20$

---

Question 29:

Simplify:
$6 \times (2^4 - 5^2) + (3^3 \div 9)$

Solution:

1. Step 1: Solve the exponents:
   $2^4 = 16$, $5^2 = 25$, and $3^3 = 27$
2. Step 2: Solve inside the parentheses:
   $16 - 25 = -9$
3. Step 3: Multiply:
   $6 \times (-9) = -54$
4. Step 4: Perform the division:
   $27 \div 9 = 3$
5. Step 5: Combine:
   $-54 + 3 = -51$

Answer: $-51$

---

Question 30:

Simplify:
$(8 \div 2) \times (3^2 - 4) + (5 + 3^2)$

Solution:

1. Step 1: Solve the exponents:
   $3^2 = 9$
2. Step 2: Solve inside the parentheses:
   $9 - 4 = 5$ and $5 + 9 = 14$
3. Step 3: Perform the division:
   $8 \div 2 = 4$
4. Step 4: Multiply:
   $4 \times 5 = 20$
5. Step 5: Combine:
   $20 + 14 = 34$

Answer: $34$