Basic Math Examples

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

Step 1

Move $32^{- \frac{3}{5}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $27$ as $3^{3}$ .

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

Step 2.2

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

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

Step 2.3

Cancel the common factor of $3$ .

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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:

$0.013\overline{8}$