How do you simplify  (4 times 10^8)^-2?

Mar 30, 2018

$\frac{1}{16 \times {10}^{16}}$

Explanation:

${\left(4 \times {10}^{8}\right)}^{-} 2$

Apply power of a product rule,

${\left(4\right)}^{-} 2 \times {\left({10}^{8}\right)}^{-} 2$

Apply power of a power rule,

${4}^{-} 2 \times {10}^{-} 16$

Apply negative exponent law,

$\frac{1}{4} ^ 2 \times \frac{1}{{10}^{16}}$

Simplify,

$\frac{1}{16 \times {10}^{16}}$