Algebra Examples

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

Step 1

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

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

Step 2

Apply the product rule to $\frac{27}{4}$ .

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

Step 3

Simplify the numerator.

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Step 3.1

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

$\frac{{(3^{3})}^{\frac{1}{3}}}{4^{\frac{1}{3}}}$

Step 3.2

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

$\frac{3^{3 (\frac{1}{3})}}{4^{\frac{1}{3}}}$

Step 3.3

Cancel the common factor of $3$ .

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Step 3.3.1

Cancel the common factor.

$\frac{3^{3 (\frac{1}{3})}}{4^{\frac{1}{3}}}$

Step 3.3.2

Rewrite the expression.

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

Step 3.4

Evaluate the exponent.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.88988157 \dots$