Question

select the equivalent expression.
$2^{-4} =?$
choose 1 answer:
a $-2^4$
b 1

Explanation:

Step1: Apply negative exponent rule

A negative exponent means the reciprocal: $a^{-n}=\frac{1}{a^n}$, so $2^{-4}=\frac{1}{2^4}$

Step2: Calculate the denominator

$2^4=2\times2\times2\times2=16$, so $\frac{1}{2^4}=\frac{1}{16}$

Step3: Evaluate given options

Option A: $-2^4=-16$, which is not equal to $\frac{1}{16}$; Option B: $1$, which is not equal to $\frac{1}{16}$.

Note: It appears the full set of options may be missing, but based on the rule of negative exponents, $2^{-4}=\frac{1}{16}$, which is not among the provided choices A and B.

Answer:

The correct equivalent expression is $\frac{1}{16}$, which is not listed in the provided options A and B.

• A. $-2^4$ (incorrect, equals -16)
• B. $1$ (incorrect)