Basic Math Examples

${(- \frac{8}{27})}^{- \frac{2}{3}}$

Step 1

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

${(- \frac{27}{8})}^{\frac{2}{3}}$

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.1

Apply the product rule to $- \frac{27}{8}$ .

${(- 1)}^{\frac{2}{3}} {(\frac{27}{8})}^{\frac{2}{3}}$

Step 2.2

Apply the product rule to $\frac{27}{8}$ .

${(- 1)}^{\frac{2}{3}} \frac{27^{\frac{2}{3}}}{8^{\frac{2}{3}}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Rewrite $- 1$ as ${(- 1)}^{3}$ .

${({(- 1)}^{3})}^{\frac{2}{3}} \frac{27^{\frac{2}{3}}}{8^{\frac{2}{3}}}$

Step 3.2

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

${(- 1)}^{3 (\frac{2}{3})} \frac{27^{\frac{2}{3}}}{8^{\frac{2}{3}}}$

Step 3.3

Cancel the common factor of $3$ .

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Step 3.3.1

Cancel the common factor.

${(- 1)}^{3 (\frac{2}{3})} \frac{27^{\frac{2}{3}}}{8^{\frac{2}{3}}}$

Step 3.3.2

Rewrite the expression.

${(- 1)}^{2} \frac{27^{\frac{2}{3}}}{8^{\frac{2}{3}}}$

Step 3.4

Simplify the expression.

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Step 3.4.1

Raise $- 1$ to the power of $2$ .

$1 \frac{27^{\frac{2}{3}}}{8^{\frac{2}{3}}}$

Step 3.4.2

Multiply $\frac{27^{\frac{2}{3}}}{8^{\frac{2}{3}}}$ by $1$ .

$\frac{27^{\frac{2}{3}}}{8^{\frac{2}{3}}}$

Step 4

Simplify the numerator.

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Step 4.1

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

$\frac{{(3^{3})}^{\frac{2}{3}}}{8^{\frac{2}{3}}}$

Step 4.2

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

$\frac{3^{3 (\frac{2}{3})}}{8^{\frac{2}{3}}}$

Step 4.3

Cancel the common factor of $3$ .

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Step 4.3.1

Cancel the common factor.

$\frac{3^{3 (\frac{2}{3})}}{8^{\frac{2}{3}}}$

Step 4.3.2

Rewrite the expression.

$\frac{3^{2}}{8^{\frac{2}{3}}}$

Step 4.4

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

$\frac{9}{8^{\frac{2}{3}}}$

Step 5

Simplify the denominator.

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Step 5.1

Rewrite $8$ as $2^{3}$ .

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

Step 5.2

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

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

Step 5.3

Cancel the common factor of $3$ .

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Step 5.3.1

Cancel the common factor.

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

Step 5.3.2

Rewrite the expression.

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

Step 5.4

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

$\frac{9}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{4}$

Decimal Form:

$2.25$

Mixed Number Form:

$2 \frac{1}{4}$