Algebra Examples

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

Step 1

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

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

Step 2

Simplify the numerator.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Cancel the common factor of $3$ .

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Step 2.3.1

Cancel the common factor.

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

Step 2.3.2

Rewrite the expression.

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

Step 2.4

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

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

Step 3

Simplify the denominator.

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

Cancel the common factor of $3$ .

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Step 3.3.1

Cancel the common factor.

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

Step 3.3.2

Rewrite the expression.

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

Step 3.4

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

$\frac{81}{16}$