Question

Which expression is equivalent to (1/16)^-4?

The answer choices are
A) (-16)^4
B) 16^4
C) 4 square root 1/16
D) -(1/16)^-4

Answer 1

Answer: Option B. $16^4$ is the correct answer.

Explanation: Since, Given expression is $(1/16)^-4$

And, we can write $(\frac{1}{16})^{-4}= 1^{-4}/16^{-4}=1/16^{-4}$

since, we know that, $a^m=1/a^-m$

similarly, we can write, $1/16^{-4}=\frac{1}{1/16^4} =16^4$.( because, we can write,  $\frac{a}{b/c} =\frac{ac}{b}$.)

hence $(1/16)^-4=16^4$ is correct.

Answer 2

Answer:

$\large\boxed{B)\ 16^4}$

Step-by-step explanation:

$\text{Use}\ a^{-n}=\left(\dfrac{1}{a}\right)^n\\\\\left(\dfrac{1}{16}\right)^{-4}=\left(\dfrac{16}{1}\right)^4=16^4$