Evaluate (81/4)^(3/2)

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

Step 1

Apply the product rule to $\frac{81}{4}$ .

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

Step 2

Simplify the numerator.

Rewrite $81$ as $9^{2}$ .

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Raise $9$ to the power of $3$ .

$\frac{729}{4^{\frac{3}{2}}}$

Step 3

Simplify the denominator.

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

$\frac{729}{{(2^{2})}^{\frac{3}{2}}}$

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

$\frac{729}{2^{2 (\frac{3}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{729}{2^{2 (\frac{3}{2})}}$

Rewrite the expression.

$\frac{729}{2^{3}}$

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

$\frac{729}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{729}{8}$

Decimal Form:

$91.125$

Mixed Number Form:

$91 \frac{1}{8}$