Algebra Examples

${(\frac{1}{4})}^{- \frac{3}{2}}$

Step 1

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

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

Step 2

Simplify the expression.

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Step 2.1

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

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

Step 2.2

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

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

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$2^{3}$

Step 4

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

$8$