Question

evaluate the expression.
\\(\left(\frac{2^8}{2^6}\
ight)^{-3}\\)
a \\(\frac{1}{64}\\)
b 4
c 12
d 64

Explanation:

Step1: Simplify the fraction inside the parentheses

Using the exponent rule $ \frac{a^m}{a^n} = a^{m - n} $, for $ \frac{2^8}{2^6} $, we have $ 2^{8 - 6}=2^2 = 4 $. So the expression becomes $ (4)^{-3} $.

Step2: Apply the negative exponent rule

The negative exponent rule states that $ a^{-n}=\frac{1}{a^n} $. So $ 4^{-3}=\frac{1}{4^3} $.

Step3: Calculate $ 4^3 $

$ 4^3 = 4\times4\times4 = 64 $. So $ \frac{1}{4^3}=\frac{1}{64} $.

Answer:

A. $\frac{1}{64}$