Algebra Examples

$\frac{{(x^{6})}^{- 2}}{x^{3}}$

Step 1

Move ${(x^{6})}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{x^{3} {(x^{6})}^{2}}$

Step 2

Multiply the exponents in ${(x^{6})}^{2}$ .

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Step 2.1

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

$\frac{1}{x^{3} x^{6 \cdot 2}}$

Step 2.2

Multiply $6$ by $2$ .

$\frac{1}{x^{3} x^{12}}$

Step 3

Multiply $x^{3}$ by $x^{12}$ 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.

$\frac{1}{x^{3 + 12}}$

Step 3.2

Add $3$ and $12$ .

$\frac{1}{x^{15}}$