Question

which expression is equivalent to \\(\frac{2^{-1}}{2^4}\\)?

answer
\\(\circ\\ \frac{1}{32}\\) \\(\circ\\ 8\\) \\(\circ\\ \frac{1}{16}\\) \\(\circ\\ \frac{1}{8}\\)

Explanation:

Step1: Apply exponent subtraction rule

When dividing like bases, subtract exponents: $a^m / a^n = a^{m-n}$.
$\frac{2^{-1}}{2^4} = 2^{-1-4} = 2^{-5}$

Step2: Convert negative exponent to fraction

A negative exponent means reciprocal: $a^{-k} = \frac{1}{a^k}$.
$2^{-5} = \frac{1}{2^5}$

Step3: Calculate the denominator

Compute $2^5$: $2^5 = 2\times2\times2\times2\times2 = 32$.
$\frac{1}{2^5} = \frac{1}{32}$

Answer:

$\frac{1}{32}$