Evaluate (-27/8)^(4/3)

${(\frac{- 27}{8})}^{\frac{4}{3}}$

Step 1

Move the negative in front of the fraction.

${(- \frac{27}{8})}^{\frac{4}{3}}$

Step 2

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

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

${(- 1)}^{\frac{4}{3}} {(\frac{27}{8})}^{\frac{4}{3}}$

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

${(- 1)}^{\frac{4}{3}} \frac{27^{\frac{4}{3}}}{8^{\frac{4}{3}}}$

Step 3

Reduce the expression by cancelling the common factors.

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

${({(- 1)}^{3})}^{\frac{4}{3}} \frac{27^{\frac{4}{3}}}{8^{\frac{4}{3}}}$

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

${(- 1)}^{3 (\frac{4}{3})} \frac{27^{\frac{4}{3}}}{8^{\frac{4}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(- 1)}^{3 (\frac{4}{3})} \frac{27^{\frac{4}{3}}}{8^{\frac{4}{3}}}$

Rewrite the expression.

${(- 1)}^{4} \frac{27^{\frac{4}{3}}}{8^{\frac{4}{3}}}$

Simplify the expression.

Raise $- 1$ to the power of $4$ .

$1 \frac{27^{\frac{4}{3}}}{8^{\frac{4}{3}}}$

Multiply $\frac{27^{\frac{4}{3}}}{8^{\frac{4}{3}}}$ by $1$ .

$\frac{27^{\frac{4}{3}}}{8^{\frac{4}{3}}}$

Step 4

Simplify the numerator.

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

$\frac{{(3^{3})}^{\frac{4}{3}}}{8^{\frac{4}{3}}}$

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

$\frac{3^{3 (\frac{4}{3})}}{8^{\frac{4}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3^{3 (\frac{4}{3})}}{8^{\frac{4}{3}}}$

Rewrite the expression.

$\frac{3^{4}}{8^{\frac{4}{3}}}$

Raise $3$ to the power of $4$ .

$\frac{81}{8^{\frac{4}{3}}}$

Step 5

Simplify the denominator.

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

$\frac{81}{{(2^{3})}^{\frac{4}{3}}}$

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

$\frac{81}{2^{3 (\frac{4}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{81}{2^{3 (\frac{4}{3})}}$

Rewrite the expression.

$\frac{81}{2^{4}}$

Raise $2$ to the power of $4$ .

$\frac{81}{16}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{81}{16}$

Decimal Form:

$5.0625$

Mixed Number Form:

$5 \frac{1}{16}$

Evaluate (-27/8)^(4/3)

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