Basic Math Examples

\frac{32^{- \frac{3}{5}}}{27^{\frac{2}{3}}}

$\frac{32^{- \frac{3}{5}}}{27^{\frac{2}{3}}}$

Step 1

Move

32^{- \frac{3}{5}}

$32^{- \frac{3}{5}}$ to the denominator using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

\frac{1}{27^{\frac{2}{3}} \cdot 32^{\frac{3}{5}}}

$\frac{1}{27^{\frac{2}{3}} \cdot 32^{\frac{3}{5}}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite

27

$27$ as

3^{3}

$3^{3}$ .

\frac{1}{{(3^{3})}^{\frac{2}{3}} \cdot 32^{\frac{3}{5}}}

$\frac{1}{{(3^{3})}^{\frac{2}{3}} \cdot 32^{\frac{3}{5}}}$

Step 2.2

Apply the power rule and multiply exponents,

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

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

\frac{1}{3^{3 (\frac{2}{3})} \cdot 32^{\frac{3}{5}}}

$\frac{1}{3^{3 (\frac{2}{3})} \cdot 32^{\frac{3}{5}}}$

Step 2.3

Cancel the common factor of

3

$3$ .

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Step 2.3.1

Cancel the common factor.

$\frac{1}{3^{3 (\frac{2}{3})} \cdot 32^{\frac{3}{5}}}$

Step 2.3.2

Rewrite the expression.

$\frac{1}{3^{2} \cdot 32^{\frac{3}{5}}}$

Step 2.4

Raise

$3$ to the power of

$2$ .

$\frac{1}{9 \cdot 32^{\frac{3}{5}}}$

Step 2.5

Rewrite

$32$ as

$2^{5}$ .

$\frac{1}{9 \cdot {(2^{5})}^{\frac{3}{5}}}$

Step 2.6

Apply the power rule and multiply exponents,

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

$\frac{1}{9 \cdot 2^{5 (\frac{3}{5})}}$

Step 2.7

Cancel the common factor of

$5$ .

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Step 2.7.1

Cancel the common factor.

$\frac{1}{9 \cdot 2^{5 (\frac{3}{5})}}$

Step 2.7.2

Rewrite the expression.

$\frac{1}{9 \cdot 2^{3}}$

Step 2.8

Raise

$2$ to the power of

$3$ .

$\frac{1}{9 \cdot 8}$

Step 3

Multiply

$9$ by

$8$ .

$\frac{1}{72}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{72}$

Decimal Form:

$0.013\overline{8}$