Simplify (5^-2)^5*5^4

${(5^{- 2})}^{5} \cdot 5^{4}$

Multiply the exponents in ${(5^{- 2})}^{5}$ .

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

$5^{- 2 \cdot 5} \cdot 5^{4}$

Multiply $- 2$ by $5$ .

$5^{- 10} \cdot 5^{4}$

Multiply $5^{- 10}$ by $5^{4}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$5^{- 10 + 4}$

Add $- 10$ and $4$ .

$5^{- 6}$

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

$\frac{1}{5^{6}}$

Raise $5$ to the power of $6$ .

$\frac{1}{15625}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{15625}$

Decimal Form:

$6.4 \cdot 10^{- 5}$