Divide (5^-5)/(5^8)

$\frac{5^{- 5}}{5^{8}}$

Step 1

Move $5^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{5^{8} \cdot 5^{5}}$

Step 2

Multiply $5^{8}$ by $5^{5}$ by adding the exponents.

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

$\frac{1}{5^{8 + 5}}$

Add $8$ and $5$ .

$\frac{1}{5^{13}}$

Step 3

Raise $5$ to the power of $13$ .

$\frac{1}{1220703125}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{1220703125}$

Decimal Form:

$8.192 \cdot 10^{- 10}$