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

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

Step 1

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

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

Step 2

Simplify the numerator.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

$\frac{8}{81^{\frac{3}{2}}}$

Step 3

Simplify the denominator.

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

$\frac{8}{{(9^{2})}^{\frac{3}{2}}}$

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

$\frac{8}{9^{2 (\frac{3}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{8}{9^{2 (\frac{3}{2})}}$

Rewrite the expression.

$\frac{8}{9^{3}}$

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

$\frac{8}{729}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{729}$

Decimal Form:

$0.01097393 \dots$