Basic Math Examples

${(\frac{243}{32})}^{- \frac{3}{5}}$

Step 1

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

${(\frac{32}{243})}^{\frac{3}{5}}$

Step 2

Apply the product rule to $\frac{32}{243}$ .

$\frac{32^{\frac{3}{5}}}{243^{\frac{3}{5}}}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $32$ as $2^{5}$ .

$\frac{{(2^{5})}^{\frac{3}{5}}}{243^{\frac{3}{5}}}$

Step 3.2

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

$\frac{2^{5 (\frac{3}{5})}}{243^{\frac{3}{5}}}$

Step 3.3

Cancel the common factor of $5$ .

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Step 3.3.1

Cancel the common factor.

$\frac{2^{5 (\frac{3}{5})}}{243^{\frac{3}{5}}}$

Step 3.3.2

Rewrite the expression.

$\frac{2^{3}}{243^{\frac{3}{5}}}$

Step 3.4

Raise $2$ to the power of $3$ .

$\frac{8}{243^{\frac{3}{5}}}$

Step 4

Simplify the denominator.

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Step 4.1

Rewrite $243$ as $3^{5}$ .

$\frac{8}{{(3^{5})}^{\frac{3}{5}}}$

Step 4.2

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

$\frac{8}{3^{5 (\frac{3}{5})}}$

Step 4.3

Cancel the common factor of $5$ .

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Step 4.3.1

Cancel the common factor.

$\frac{8}{3^{5 (\frac{3}{5})}}$

Step 4.3.2

Rewrite the expression.

$\frac{8}{3^{3}}$

Step 4.4

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

$\frac{8}{27}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{27}$

Decimal Form:

$0.\overline{296}$