Question

Find the equivalent expression of 16^-2

Answer 1

Find the equivalent expression of

$16^{-2}$

First, we take advantage of the fact that 16 is a perfect square:

$(4^2)^{-2}$

But 4 is also a perfect square:

$((2^2)^2)^{-2}$

Now apply the power rule of exponents. We multiply all of them:

$2^{-8}$

Now we apply the rule of negative exponents:

$2^{-8}=\frac{1}{2^8}$

This is an equivalent expression, but if it's required to compute the result of the power, the final expression is:

$\frac{1}{2^8}=\frac{1}{256}$