Basic Math Examples

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

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

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

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

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

Step 2

Apply the product rule to

\frac{9}{4}

$\frac{9}{4}$ .

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

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

Step 3

Simplify the numerator.

Tap for more steps...

Step 3.1

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

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

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

Step 3.2

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

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

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

Step 3.3

Cancel the common factor of

2

$2$ .

Tap for more steps...

Step 3.3.1

Cancel the common factor.

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

Step 3.3.2

Rewrite the expression.

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

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

Step 3.4

Raise

$3$ to the power of

$3$ .

$\frac{27}{4^{\frac{3}{2}}}$

$\frac{27}{4^{\frac{3}{2}}}$

Step 4

Simplify the denominator.

Tap for more steps...

Step 4.1

Rewrite

$4$ as

$2^{2}$ .

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

Step 4.2

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

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

Step 4.3

Cancel the common factor of

$2$ .

Tap for more steps...

Step 4.3.1

Cancel the common factor.

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

Step 4.3.2

Rewrite the expression.

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

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

Step 4.4

Raise

$2$ to the power of

$3$ .

$\frac{27}{8}$

$\frac{27}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{27}{8}$

Decimal Form:

$3.375$

Mixed Number Form:

$3 \frac{3}{8}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$