Evaluate (81/16)^(3/4)

${(\frac{81}{16})}^{\frac{3}{4}}$

Step 1

Apply the product rule to $\frac{81}{16}$ .

$\frac{81^{\frac{3}{4}}}{16^{\frac{3}{4}}}$

Step 2

Simplify the numerator.

Rewrite $81$ as $3^{4}$ .

$\frac{{(3^{4})}^{\frac{3}{4}}}{16^{\frac{3}{4}}}$

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

$\frac{3^{4 (\frac{3}{4})}}{16^{\frac{3}{4}}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{3^{4 (\frac{3}{4})}}{16^{\frac{3}{4}}}$

Rewrite the expression.

$\frac{3^{3}}{16^{\frac{3}{4}}}$

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

$\frac{27}{16^{\frac{3}{4}}}$

Step 3

Simplify the denominator.

Rewrite $16$ as $2^{4}$ .

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

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

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{27}{2^{3}}$

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

$\frac{27}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{27}{8}$

Decimal Form:

$3.375$

Mixed Number Form:

$3 \frac{3}{8}$