Simplify (5^-2(3)^-2)/(6^-1)

$\frac{5^{- 2} {(3)}^{- 2}}{6^{- 1}}$

Step 1

Simplify the expression.

Move $5^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{{(3)}^{- 2}}{6^{- 1} \cdot 5^{2}}$

Move ${(3)}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{6^{- 1} \cdot 5^{2} \cdot 3^{2}}$

Move $6^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{6}{5^{2} \cdot 3^{2}}$

Step 2

Simplify the denominator.

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

$\frac{6}{25 \cdot 3^{2}}$

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

$\frac{6}{25 \cdot 9}$

Step 3

Reduce the expression by cancelling the common factors.

Multiply $25$ by $9$ .

$\frac{6}{225}$

Cancel the common factor of $6$ and $225$ .

Factor $3$ out of $6$ .

$\frac{3 (2)}{225}$

Cancel the common factors.

Factor $3$ out of $225$ .

$\frac{3 \cdot 2}{3 \cdot 75}$

Cancel the common factor.

$\frac{3 \cdot 2}{3 \cdot 75}$

Rewrite the expression.

$\frac{2}{75}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{75}$

Decimal Form:

$0.02\overline{6}$