Simplify the Radical Expression (27/8)^(4/3)

${(\frac{27}{8})}^{\frac{4}{3}}$

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

$\frac{27^{\frac{4}{3}}}{8^{\frac{4}{3}}}$

Simplify the numerator.

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

$\frac{{(3^{3})}^{\frac{4}{3}}}{8^{\frac{4}{3}}}$

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

$\frac{3^{3 (\frac{4}{3})}}{8^{\frac{4}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3^{3 (\frac{4}{3})}}{8^{\frac{4}{3}}}$

Rewrite the expression.

$\frac{3^{4}}{8^{\frac{4}{3}}}$

Raise $3$ to the power of $4$ .

$\frac{81}{8^{\frac{4}{3}}}$

Simplify the denominator.

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

$\frac{81}{{(2^{3})}^{\frac{4}{3}}}$

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

$\frac{81}{2^{3 (\frac{4}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{81}{2^{3 (\frac{4}{3})}}$

Rewrite the expression.

$\frac{81}{2^{4}}$

Raise $2$ to the power of $4$ .

$\frac{81}{16}$