# How do you simplify (5 × 10^8)^(–2) in scientific notation?

Jul 18, 2016

$4 \times {10}^{-} 18$

#### Explanation:

Get rid of the brackets by using the power law of indices:

${5}^{-} 2 \times {10}^{-} 16$

Get rid of the negative indices using: $\text{ } {x}^{-} m = \frac{1}{x} ^ m$

1/(5^2 xx 10^16

=$\frac{1}{25 \times {10}^{16}}$

=$\frac{1}{2.5 \times 10 \times {10}^{16}}$

=$\frac{1}{2.5 \times {10}^{17}} \text{ but } \frac{1}{2.5} = \frac{10}{25} = 0.4$

=$0.4 \times {10}^{-} 17$

=$4 \times {10}^{-} 18$