Worksheet on Exponents and Powers

Solved Questions on Exponents and Powers

1. Evaluate the following expression using laws of expression:

a) 2⁻² × 5⁶ × 7² ×11⁴
b) 2⁻² ×7² × 11⁴
c) 2⁻² × 5⁶ ×11⁴
d) 2⁻⁵ × 5⁶ ×7² ×11⁴

Answer: c) 2⁻² × 5⁶ × 11⁴

Explanation: Using laws of exponents,

2. Which is the following numerical expression in scientific notation “A single drop of water has 60230000000000000000000 molecules.”?

a) 023 × 10¹⁹ molecules
b) 023 × 10²¹ molecules
c) 023 × 10²² molecules
d) 023 × 10²³ molecules

Answer: c) 6.023 × 10²² molecules

Explanation:

3. What is the value of “a” in the given equation?

(2023¹¹)^a ÷  (2023⁷)^a = (2023)¹⁰⁸

a) 21
b) 23
c) 27
d) 29

Answer: c) 27

Explanation: Using laws of exponents,

(2023¹¹)^a ÷ (2023⁷)^a = (2023)¹⁰⁸

⇒ (2023)^11×a ÷  (2023)^7×a = (2023)¹⁰⁸
⇒ (2023)^11a ÷  (2023)^7a = (2023)¹⁰⁸
⇒ (2023)^{11a − 7a} = (2023)¹⁰⁸
⇒ (2023)^4a  = (2023)¹⁰⁸

Comparing both sides

⇒ 4a = 108
⇒ a = 108/4
⇒ a = 27

4. What is the value of n in the following equation?

a) −3
b) 3
c) −5 
d) 5

Answer: b) 3

Explanation: Using laws of exponents,

Comparing both sides

⇒ n = 3

5. Simplify the following expression using laws of exponents: 

(−1)¹⁹⁹ ×[(243)³ ÷ (27)⁴]

a) −27
b) 2
c) −81
d) 81

Answer: a) −27 

Explanation: Using laws of exponents,

(−1)¹⁹⁹ × [(243)³ ÷ (27)⁴]

= (−1) × [(3⁵)³ ÷ (3³)⁴] [(−1)^odd = −1]
= (−1) × [3¹⁵ ÷ 3¹²] 
= (−1) × [3^{15 − 12}] 
= (−1) × [3³] 
= (−1) × 27 
= −27