Question

multiple-choice question
simplify \\(\frac{2^{-5}}{2^{2}}\\)
\\(2^{-7}\\)
\\(\frac{1}{2^{7}}\\)
\\(2^{-3}\\)

Explanation:

Step1: Apply exponent division rule

When dividing exponents with the same base, subtract the denominator exponent from the numerator exponent: $a^m / a^n = a^{m-n}$.
$\frac{2^{-5}}{2^{2}} = 2^{-5-2}$

Step2: Calculate the exponent

Compute the value of the subtracted exponent.
$2^{-5-2} = 2^{-7}$

Step3: Rewrite negative exponent

A negative exponent can be rewritten as a positive exponent in the denominator: $a^{-k} = \frac{1}{a^k}$.
$2^{-7} = \frac{1}{2^7}$

Answer:

$2^{-7}$, $\frac{1}{2^7}$