Simplify (8/27)^(2/3)*(3/2)^2

${(\frac{8}{27})}^{\frac{2}{3}} \cdot {(\frac{3}{2})}^{2}$

Apply the product rule to $\frac{8}{27}$ .

$\frac{8^{\frac{2}{3}}}{27^{\frac{2}{3}}} \cdot {(\frac{3}{2})}^{2}$

Simplify the numerator.

Rewrite $8$ as $2^{3}$ .

$\frac{{(2^{3})}^{\frac{2}{3}}}{27^{\frac{2}{3}}} \cdot {(\frac{3}{2})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{2^{3 (\frac{2}{3})}}{27^{\frac{2}{3}}} \cdot {(\frac{3}{2})}^{2}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{2^{3 (\frac{2}{3})}}{27^{\frac{2}{3}}} \cdot {(\frac{3}{2})}^{2}$

Rewrite the expression.

$\frac{2^{2}}{27^{\frac{2}{3}}} \cdot {(\frac{3}{2})}^{2}$

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

$\frac{4}{27^{\frac{2}{3}}} \cdot {(\frac{3}{2})}^{2}$

Simplify the denominator.

Rewrite $27$ as $3^{3}$ .

$\frac{4}{{(3^{3})}^{\frac{2}{3}}} \cdot {(\frac{3}{2})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{4}{3^{3 (\frac{2}{3})}} \cdot {(\frac{3}{2})}^{2}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{4}{3^{3 (\frac{2}{3})}} \cdot {(\frac{3}{2})}^{2}$

Rewrite the expression.

$\frac{4}{3^{2}} \cdot {(\frac{3}{2})}^{2}$

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

$\frac{4}{9} \cdot {(\frac{3}{2})}^{2}$

Combine fractions.

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

$\frac{4}{9} \cdot \frac{3^{2}}{2^{2}}$

Combine.

$\frac{4 \cdot 3^{2}}{9 \cdot 2^{2}}$

Simplify the expression.

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

$\frac{4 \cdot 9}{9 \cdot 2^{2}}$

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

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

Multiply $4$ by $9$ .

$\frac{36}{9 \cdot 4}$

Multiply $9$ by $4$ .

$\frac{36}{36}$

Divide $36$ by $36$ .

$1$