Evaluate (9/100)^(3/2)

${(\frac{9}{100})}^{\frac{3}{2}}$

Step 1

Apply the product rule to $\frac{9}{100}$ .

$\frac{9^{\frac{3}{2}}}{100^{\frac{3}{2}}}$

Step 2

Simplify the numerator.

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

$\frac{{(3^{2})}^{\frac{3}{2}}}{100^{\frac{3}{2}}}$

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

$\frac{3^{2 (\frac{3}{2})}}{100^{\frac{3}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3^{2 (\frac{3}{2})}}{100^{\frac{3}{2}}}$

Rewrite the expression.

$\frac{3^{3}}{100^{\frac{3}{2}}}$

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

$\frac{27}{100^{\frac{3}{2}}}$

Step 3

Simplify the denominator.

Rewrite $100$ as $10^{2}$ .

$\frac{27}{{(10^{2})}^{\frac{3}{2}}}$

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

$\frac{27}{10^{2 (\frac{3}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{27}{10^{2 (\frac{3}{2})}}$

Rewrite the expression.

$\frac{27}{10^{3}}$

Raise $10$ to the power of $3$ .

$\frac{27}{1000}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{27}{1000}$

Decimal Form:

$0.027$