Mathematics: Exponents QA

Class 9 – Powers and Exponents

Step-by-Step Solutions

1. Simplify

(2⁵ × 3⁴ × 5²) / (2³ × 3² × 5)

2⁵⁻³ × 3⁴⁻² × 5²⁻¹
= 2² × 3² × 5
= 4 × 9 × 5 = 180
Answer: 180

2. Simplify

(3⁻² × 9³) / 27

9 = 3², 27 = 3³
= (3⁻² × (3²)³) / 3³
= (3⁻² × 3⁶) / 3³
= 3¹ = 3
Answer: 3

3. Evaluate

(2³ × 5⁻¹) / 10⁻²

2³ = 8, 5⁻¹ = 1/5
= (8/5) ÷ (1/100)
= (8/5) × 100
= 160
Answer: 160

4. Simplify

((a³b⁻²) / (a⁻¹b⁴))²

= (a⁴b⁻⁶)²
= a⁸b⁻¹²
= a⁸ / b¹²
Answer: a⁸ / b¹²

5. Find x

3^2x = 81^x−1

81 = 3⁴
3^2x = 3^4x−4
2x = 4x − 4
x = 2
Answer: x = 2

6. Simplify

((4³)² × 8⁻¹) / 2⁵

4 = 2², 8 = 2³
= 2¹² × 2⁻³ / 2⁵
= 2⁴ = 16
Answer: 16

7. Given

a²b³ = 72 and ab = 6

(a²b³) / (ab) = 72 / 6
ab² = 12
Answer: 12

8. Simplify

((x⁻²y³)³) / (x⁴y⁻²)

= x⁻⁶y⁹ / x⁴y⁻²
= x⁻¹⁰y¹¹
= y¹¹ / x¹⁰
Answer: y¹¹ / x¹⁰

9. Evaluate

(125^2/3 × 16^3/4) / 25^1/2

125 = 5³, 16 = 2⁴, 25 = 5²
= 25 × 8 / 5
= 40
Answer: 40

10. Solve

2^x+1 + 2^x = 96

2 × 2^x + 2^x = 96
3 × 2^x = 96
2^x = 32
x = 5
Answer: x = 5