Precalculus Examples

$\ln (\frac{\sqrt{a b^{8}}}{c})$

Step 1

Rewrite $a b^{8}$ as ${({(b^{2})}^{2})}^{2} a$ .

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Step 1.1

Rewrite $b^{8}$ as ${(b^{4})}^{2}$ .

$\ln (\frac{\sqrt{a {(b^{4})}^{2}}}{c})$

Step 1.2

Reorder $a$ and ${(b^{4})}^{2}$ .

$\ln (\frac{\sqrt{{(b^{4})}^{2} a}}{c})$

Step 1.3

Rewrite $b^{4}$ as ${(b^{2})}^{2}$ .

$\ln (\frac{\sqrt{{({(b^{2})}^{2})}^{2} a}}{c})$

Step 2

Pull terms out from under the radical.

$\ln (\frac{{(b^{2})}^{2} \sqrt{a}}{c})$

Step 3

Multiply the exponents in ${(b^{2})}^{2}$ .

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Step 3.1

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

$\ln (\frac{b^{2 \cdot 2} \sqrt{a}}{c})$

Step 3.2

Multiply $2$ by $2$ .

$\ln (\frac{b^{4} \sqrt{a}}{c})$