Precalculus Examples

$(\sqrt{h^{4} + 1}) (\sqrt{h^{4} + 1^{- 1}})$

Step 1

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

$\sqrt{h^{4} + 1} \sqrt{h^{4} + \frac{1}{1}}$

Step 2

Divide $1$ by $1$ .

$\sqrt{h^{4} + 1} \sqrt{h^{4} + 1}$

Step 3

Multiply $\sqrt{h^{4} + 1} \sqrt{h^{4} + 1}$ .

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Step 3.1

Raise $\sqrt{h^{4} + 1}$ to the power of $1$ .

${\sqrt{h^{4} + 1}}^{1} \sqrt{h^{4} + 1}$

Step 3.2

Raise $\sqrt{h^{4} + 1}$ to the power of $1$ .

${\sqrt{h^{4} + 1}}^{1} {\sqrt{h^{4} + 1}}^{1}$

Step 3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${\sqrt{h^{4} + 1}}^{1 + 1}$

Step 3.4

Add $1$ and $1$ .

${\sqrt{h^{4} + 1}}^{2}$

Step 4

Rewrite ${\sqrt{h^{4} + 1}}^{2}$ as $h^{4} + 1$ .

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Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{h^{4} + 1}$ as ${(h^{4} + 1)}^{\frac{1}{2}}$ .

${({(h^{4} + 1)}^{\frac{1}{2}})}^{2}$

Step 4.2

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

${(h^{4} + 1)}^{\frac{1}{2} \cdot 2}$

Step 4.3

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

${(h^{4} + 1)}^{\frac{2}{2}}$

Step 4.4

Cancel the common factor of $2$ .

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Step 4.4.1

Cancel the common factor.

${(h^{4} + 1)}^{\frac{2}{2}}$

Step 4.4.2

Rewrite the expression.

${(h^{4} + 1)}^{1}$

Step 4.5

Simplify.

$h^{4} + 1$