Evaluate (16/9)^(3/2)

${(\frac{16}{9})}^{\frac{3}{2}}$

Step 1

Apply the product rule to $\frac{16}{9}$ .

$\frac{16^{\frac{3}{2}}}{9^{\frac{3}{2}}}$

Step 2

Simplify the numerator.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

$\frac{64}{9^{\frac{3}{2}}}$

Step 3

Simplify the denominator.

Rewrite $9$ as $3^{2}$ .

$\frac{64}{{(3^{2})}^{\frac{3}{2}}}$

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

$\frac{64}{3^{2 (\frac{3}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{64}{3^{2 (\frac{3}{2})}}$

Rewrite the expression.

$\frac{64}{3^{3}}$

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

$\frac{64}{27}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{64}{27}$

Decimal Form:

$2.\overline{370}$

Mixed Number Form:

$2 \frac{10}{27}$