Question

Consider this power. (–4) –3 1. Apply the negative exponents rule: 1 (−4)3 2. Expand the exponent: 1 (−4)(−4)(−4) 3.Simplify: What is the value of (–4)–3? Negative StartFraction 1 Over 64 EndFraction Negative StartFraction 1 Over 12 EndFraction StartFraction 1 Over 64 EndFraction StartFraction 1 Over 12 EndFraction

Answer 1

Given:

The given expression is

$(-4)^{-3}$

To find:

The value of given expression.

Solution:

We have,

$(-4)^{-3}$

Applying the negative exponents rule, we get

$(-4)^{-3}=\dfrac{1}{(-4)^3}$     $[\because a^{-n}=\dfrac{1}{a^n}]$

Expanding the exponent, we get

$(-4)^{-3}=\dfrac{1}{(-4)(-4)(-4)}$  

$(-4)^{-3}=\dfrac{1}{-64}$  

$(-4)^{-3}=-\dfrac{1}{64}$  

The value of given expression is $-\dfrac{1}{64}$.

Therefore, the correct option is A.