Law of Exponent

Law of Exponent

Power of a Power

Power of a Power

(a^m)ⁿ = a^(m)(n)

Examples

(2³)²

Solution: 2(3)(2)

let's copy the base then multiply the exponents

2(3)(2) = 26

since we have the numberical base let's expan it then evaluate

26 = 2 x 2 x 2 x 2 x 2 x 2 = 64

the final answer is 64.

(m⁴n⁵)²

Since there are 2 variables inside the quantity, let's distribute the exponent outside the quantity then apply power of a power law.

(m⁴n⁵)² = m⁽⁴⁾⁽²⁾n⁽⁵⁾⁽²⁾ = m⁸n¹⁰

the final answer is m⁸n^10.

Let's try it!

Solve the following using Power of a Power law of exponent and choose the correct answer.

Multiple Choice

(x²y)³

• x⁵y³

• x⁶y³

Multiple Choice

(3²)²

• 3⁴

• 3

Multiple Choice

(2b⁴c⁵)²

• 2b⁸c¹⁰

• 4b⁸c¹⁰

Multiple Choice

(2b⁴c⁵)²

• 2b⁸c¹⁰

• 4b⁸c¹⁰