Simplify 5^-1(3^-2)

$5^{- 1} (3^{- 2})$

Step 1

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

$\frac{1}{5} \cdot 3^{- 2}$

Step 2

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

$\frac{1}{5} \cdot \frac{1}{3^{2}}$

Step 3

Combine.

$\frac{1 \cdot 1}{5 \cdot 3^{2}}$

Step 4

Simplify the expression.

Multiply $1$ by $1$ .

$\frac{1}{5 \cdot 3^{2}}$

Raise $3$ to the power of $2$ .

$\frac{1}{5 \cdot 9}$

Multiply $5$ by $9$ .

$\frac{1}{45}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{45}$

Decimal Form:

$0.0\overline{2}$