Algebra Examples

${(\frac{c^{4}}{c^{8}})}^{\frac{3}{4}}$

Step 1

Cancel the common factor of $c^{4}$ and $c^{8}$ .

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Step 1.1

Multiply by $1$ .

${(\frac{c^{4} \cdot 1}{c^{8}})}^{\frac{3}{4}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $c^{4}$ out of $c^{8}$ .

${(\frac{c^{4} \cdot 1}{c^{4} c^{4}})}^{\frac{3}{4}}$

Step 1.2.2

Cancel the common factor.

${(\frac{c^{4} \cdot 1}{c^{4} c^{4}})}^{\frac{3}{4}}$

Step 1.2.3

Rewrite the expression.

${(\frac{1}{c^{4}})}^{\frac{3}{4}}$

Step 2

Simplify the expression.

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Step 2.1

Apply the product rule to $\frac{1}{c^{4}}$ .

$\frac{1^{\frac{3}{4}}}{{(c^{4})}^{\frac{3}{4}}}$

Step 2.2

One to any power is one.

$\frac{1}{{(c^{4})}^{\frac{3}{4}}}$

Step 2.3

Multiply the exponents in ${(c^{4})}^{\frac{3}{4}}$ .

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Step 2.3.1

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

$\frac{1}{c^{4 (\frac{3}{4})}}$

Step 2.3.2

Cancel the common factor of $4$ .

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Step 2.3.2.1

Cancel the common factor.

$\frac{1}{c^{4 (\frac{3}{4})}}$

Step 2.3.2.2

Rewrite the expression.

$\frac{1}{c^{3}}$