Worksheet on Exponents and Powers

Solved Questions on Exponents and Powers

1. What is the multiplicative inverse of the following expression?

a) ⁶⁴⁄₇₂₉
b) ¹²⁸⁄₇₂₉
c) ⁷²⁹⁄₆₄
d) ⁷²⁹⁄₁₂₈

Answer: a) ⁶⁴⁄₇₂₉

Explanation: 

Thus, the multiplicative inverse of 729/64 is 64/729.

2. Which of the following exponents in expanded form represents the number 5629.354?

a) 5 × 10⁴ + 6 × 10³ + 2 × 10² + 9 × 10¹ + 3 × 10⁻¹ + 5 × 10⁻² + 4 × 10⁻³
b) 5 × 10⁴ + 6 × 10³ + 2 × 10² + 9 × 10⁻¹ + 3 × 10⁻² + 5 × 10⁻³ + 4 × 10⁻⁴
c) 5 × 10³ + 6 × 10² + 2 × 10¹ + 9 × 10⁰ + 3 × 10⁻¹ + 5 × 10⁻² + 4 × 10⁻³
d) 5 × 10³ + 6 × 10² + 2 × 10¹ + 9 × 10⁻¹ + 3 × 10⁻² + 5 × 10⁻³ + 4 × 10⁻⁴

Answer: c) 5 × 10³ + 6 × 10² + 2 × 10¹ + 9 × 10⁰ + 3 × 10⁻¹ + 5 × 10⁻² + 4 × 10⁻³  

Explanation: The expanded form of 5629.354

= 5 × 10³ + 6 × 10² + 2 × 10¹ + 9 × 10⁰ + 3 × 10⁻¹ + 5 × 10⁻² + 4 × 10⁻³

3. Simplify the following expression: (− 7/3)⁻² × (7/9)² ÷ (2/7)⁻² × 42

a) ⁴⁄₂₁
b) ²¹⁄₄
c) ⁸⁄₂₁
d) ²¹⁄₈

Answer: c) ⁸⁄₂₁

Explanation:

4. What is the value of ‘p’ if 11^{2p + 11} = 1/1331?

a) 7
b) −7
c) 11
d) −11

Answer: b)  −7

Explanation:

5. What is the area of a rectangle in standard form whose length is 17 × 105 m and breadth is  1.7 × 104  m?

a) 2.89 × 10⁻⁹ m²
b) 2.89 × 10⁹ m²
c) 2.89 × 10⁻¹⁰ m²
d) 2.89 × 10¹⁰ m²

Answer: d) 2.89 × 10¹⁰ m²

Explanation: