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

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

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Apply the product rule to $\frac{3}{2}$ .

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

Combine.

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

Simplify the expression.

Multiply $3^{2}$ by $1$ .

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

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

$\frac{3^{2}}{6 \cdot 4}$

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

$\frac{9}{6 \cdot 4}$

Multiply $6$ by $4$ .

$\frac{9}{24}$

Cancel the common factor of $9$ and $24$ .

Factor $3$ out of $9$ .

$\frac{3 (3)}{24}$

Cancel the common factors.

Factor $3$ out of $24$ .

$\frac{3 \cdot 3}{3 \cdot 8}$

Cancel the common factor.

$\frac{3 \cdot 3}{3 \cdot 8}$

Rewrite the expression.

$\frac{3}{8}$

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{8}$

Decimal Form:

$0.375$