Find the Exact Value 5^-5*5^3

$5^{- 5} \cdot 5^{3}$

Step 1

Multiply $5^{- 5}$ by $5^{3}$ by adding the exponents.

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

$5^{- 5 + 3}$

Add $- 5$ and $3$ .

$5^{- 2}$

Step 2

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

$\frac{1}{5^{2}}$

Step 3

Raise $5$ to the power of $2$ .

$\frac{1}{25}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{25}$

Decimal Form:

$0.04$