## Questions and Answers

What is the value of 2^3 × 2^5?

128

If x^(-2) = 1/16, what is the value of x?

2

What is the value of (3^2)^4?

6561

If a^2 = 16, what is the value of a^5?

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What is the value of (2^3)^(-2) × 2^5?

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What is the value of (5^2)^3?

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If x^3 = 27, what is the value of x^(3/2)?

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What is the value of (2^(-3))^(-2)?

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If a^3 = 64, what is the value of a^(5/3)?

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What is the value of (3^2) × (3^(-3))?

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## Study Notes

### Exponents and Powers

- 2^3 × 2^5 = 2^(3+5) = 2^8

### Solving for x in x^(-2) = 1/16

- x^(-2) = 1/16 => x^2 = 16 => x = ±4

### Powers of Powers

- (3^2)^4 = 3^(2×4) = 3^8

### Solving for a in a^2 = 16

- a^2 = 16 => a = ±4 => a^5 = (±4)^5 = ±1024

### Simplifying Expressions

- (2^3)^(-2) × 2^5 = 2^(-3×2) × 2^5 = 2^(-6) × 2^5 = 2^(-1) = 1/2

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## Description

Test your understanding of exponents and powers with these questions from Class 8 ICSE foundation mathematics. Topics include calculating values of exponential expressions and solving equations involving powers.