Algebra Examples

${(\frac{16}{3})}^{- \frac{3}{4}}$

Step 1

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

${(\frac{3}{16})}^{\frac{3}{4}}$

Step 2

Apply the product rule to $\frac{3}{16}$ .

$\frac{3^{\frac{3}{4}}}{16^{\frac{3}{4}}}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $16$ as $2^{4}$ .

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

Step 3.2

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

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

Step 3.3

Cancel the common factor of $4$ .

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Step 3.3.1

Cancel the common factor.

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

Step 3.3.2

Rewrite the expression.

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

Step 3.4

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.28493838 \dots$