Question

which expression is equivalent to $\frac{10^{-6}}{5^{-6}}$?
$\frac{1}{2^{6}}$
$\frac{1}{2^{-6}}$
$2^{0}$
$2$

Explanation:

Step1: Split numerator into factors

$\frac{10^{-6}}{5^{-6}} = \frac{(2 \times 5)^{-6}}{5^{-6}}$

Step2: Apply exponent product rule

$\frac{2^{-6} \times 5^{-6}}{5^{-6}}$

Step3: Cancel like terms

$2^{-6}$

Step4: Rewrite negative exponent

$2^{-6} = \frac{1}{2^{6}}$

Answer:

$\frac{1}{2^6}$