Algebra Examples

$\frac{1}{{(\sqrt{2})}^{5}}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$\frac{1}{{(2^{\frac{1}{2}})}^{5}}$

Step 2

Multiply the exponents in ${(2^{\frac{1}{2}})}^{5}$ .

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Step 2.1

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

$\frac{1}{2^{\frac{1}{2} \cdot 5}}$

Step 2.2

Combine $\frac{1}{2}$ and $5$ .

$\frac{1}{2^{\frac{5}{2}}}$