Question

Can you please show work

Answer 1

The expression B. $\frac{1}{9^{16} }$ is equivalent to $(9^{-2}) ^{8} .$

Step-by-step explanation:

Step 1:

For the given number, -2 and 8 are both exponents.

According to the power rule, $(a^{x}) ^{y} = a^{xy}$.

Here a is 9, x is -2 and y is 8.

Substituting the values, we get $(9^{-2}) ^{8} = 9^{(-2)(8)} .$

$9^{(-2)(8)} = 9^{-16} .$

Step 2:

According to the negative exponent rule, we have $a^{-z} = \frac{1}{a^{z} } .$

Here a is 9 whereas z is equal to 16.

So $9^{-16} = \frac{1}{9^{16} } .$

This is represented by option B.