Algebra Examples

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

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Combine $2^{\frac{1}{2}}$ and $\frac{1}{x^{2}}$ .

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

Step 3

Move the negative in front of the fraction.

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

Step 4

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

${(\frac{x^{2}}{2^{\frac{1}{2}}})}^{\frac{2}{3}}$

Step 5

Apply the product rule to $\frac{x^{2}}{2^{\frac{1}{2}}}$ .

$\frac{{(x^{2})}^{\frac{2}{3}}}{{(2^{\frac{1}{2}})}^{\frac{2}{3}}}$

Step 6

Multiply the exponents in ${(x^{2})}^{\frac{2}{3}}$ .

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Step 6.1

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

$\frac{x^{2 (\frac{2}{3})}}{{(2^{\frac{1}{2}})}^{\frac{2}{3}}}$

Step 6.2

Multiply $2 (\frac{2}{3})$ .

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Step 6.2.1

Combine $2$ and $\frac{2}{3}$ .

$\frac{x^{\frac{2 \cdot 2}{3}}}{{(2^{\frac{1}{2}})}^{\frac{2}{3}}}$

Step 6.2.2

Multiply $2$ by $2$ .

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

Step 7

Multiply the exponents in ${(2^{\frac{1}{2}})}^{\frac{2}{3}}$ .

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Step 7.1

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

$\frac{x^{\frac{4}{3}}}{2^{\frac{1}{2} \cdot \frac{2}{3}}}$

Step 7.2

Cancel the common factor of $2$ .

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Step 7.2.1

Cancel the common factor.

$\frac{x^{\frac{4}{3}}}{2^{\frac{1}{2} \cdot \frac{2}{3}}}$

Step 7.2.2

Rewrite the expression.

$\frac{x^{\frac{4}{3}}}{2^{\frac{1}{3}}}$