Simplify Exponents - Multiplying Answers and Explanations

Link to Simplify Exponents - Multiplying  Answers and Explanations

Simplify the following:

1. (x^-3)^-5 = x¹⁵

Keep the base and multiply the exponents.

(x^-3)^-5 = x^{-3 * -5} = x¹⁵

 

2. (2⁵)⁵ = 2²⁵

Keep the base and multiply the exponents.

(2⁵)⁵ = 2^{5 * 5} = 2²⁵

 

3. (10^x)^y = 10^xy

Keep the base and multiply the exponents.

(10^x)^y = 10^{x * y} = 10^xy

4. (-8³)^{(x + 1)} =  (-8)^{3x + 3}

Keep the base and multiply the exponents.

(-8³)^{(x + 1)} = -8^{3(x + 1)}

Distribute the 3.

(-8)^{3(x + 1)}= (-8)^{3 * x + 3 * 1} = (-8)^{3x + 3}

 

5. (p⁴)^¼ = p

Keep the base and multiply the exponents.

p^{4 * ¼} = p¹ = p

 

6. (e^x)² = e^2x

Keep the base and multiply the exponents.

e^{x * 2} = e^2x