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

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

Step 1

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

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

Step 2

Simplify the numerator.

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

$\frac{{(10^{2})}^{\frac{3}{2}}}{9^{\frac{3}{2}}}$

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

$\frac{10^{2 (\frac{3}{2})}}{9^{\frac{3}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{10^{2 (\frac{3}{2})}}{9^{\frac{3}{2}}}$

Rewrite the expression.

$\frac{10^{3}}{9^{\frac{3}{2}}}$

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

$\frac{1000}{9^{\frac{3}{2}}}$

Step 3

Simplify the denominator.

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

$\frac{1000}{{(3^{2})}^{\frac{3}{2}}}$

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

$\frac{1000}{3^{2 (\frac{3}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{1000}{3^{2 (\frac{3}{2})}}$

Rewrite the expression.

$\frac{1000}{3^{3}}$

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

$\frac{1000}{27}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1000}{27}$

Decimal Form:

$37.\overline{037}$

Mixed Number Form:

$37 \frac{1}{27}$