Simplify (10^-2)^4

${(10^{- 2})}^{4}$

Multiply the exponents in ${(10^{- 2})}^{4}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$10^{- 2 \cdot 4}$

Multiply $- 2$ by $4$ .

$10^{- 8}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{10^{8}}$

Raise $10$ to the power of $8$ .

$\frac{1}{100000000}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{100000000}$

Decimal Form:

$1 \cdot 10^{- 8}$