Evaluate (-8/27)^(2/3)

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

Step 1

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

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

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

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

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

Step 2

Reduce the expression by cancelling the common factors.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the expression.

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

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

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

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

Step 3

Simplify the numerator.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 4

Simplify the denominator.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

$\frac{4}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{9}$

Decimal Form:

$0.\overline{4}$

Evaluate (-8/27)^(2/3)

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