Question

Simplify the expression. [(–5)–7 (–5)8]3

1. Apply the product of powers:   [(–5)1]3

2. Apply the power of a power:   (–5)3

3. Simplify:

What is the value of the expression?

Answer 1

Interpret the expression as [(-5)^{-7}·(-5)^8]^3.

1. Product of powers: (-5)^{-7}·(-5)^8 = (-5)^{-7+8} = (-5)^1.
2. Power of a power: [(-5)^1]^3 = (-5)^{1·3} = (-5)^3.
3. Compute: (-5)^3 = -125.

So the value is -125.