Algebra Examples

$\frac{{(x^{12})}^{\frac{1}{3}}}{x^{- 6}}$

Step 1

Move $x^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(x^{12})}^{\frac{1}{3}} x^{6}$

Step 2

Multiply the exponents in ${(x^{12})}^{\frac{1}{3}}$ .

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Step 2.1

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

$x^{12 (\frac{1}{3})} x^{6}$

Step 2.2

Cancel the common factor of $3$ .

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Step 2.2.1

Factor $3$ out of $12$ .

$x^{3 (4) \frac{1}{3}} x^{6}$

Step 2.2.2

Cancel the common factor.

$x^{3 \cdot 4 \frac{1}{3}} x^{6}$

Step 2.2.3

Rewrite the expression.

$x^{4} x^{6}$

Step 3

Multiply $x^{4}$ by $x^{6}$ by adding the exponents.

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Step 3.1

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

$x^{4 + 6}$

Step 3.2

Add $4$ and $6$ .

$x^{10}$