Algebra Examples

${(\frac{x^{- 10}}{x^{5}})}^{\frac{2}{5}}$

Step 1

Move $x^{- 10}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{1}{x^{5} x^{10}})}^{\frac{2}{5}}$

Step 2

Multiply $x^{5}$ by $x^{10}$ by adding the exponents.

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Step 2.1

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

${(\frac{1}{x^{5 + 10}})}^{\frac{2}{5}}$

Step 2.2

Add $5$ and $10$ .

${(\frac{1}{x^{15}})}^{\frac{2}{5}}$

Step 3

Apply the product rule to $\frac{1}{x^{15}}$ .

$\frac{1^{\frac{2}{5}}}{{(x^{15})}^{\frac{2}{5}}}$

Step 4

One to any power is one.

$\frac{1}{{(x^{15})}^{\frac{2}{5}}}$

Step 5

Multiply the exponents in ${(x^{15})}^{\frac{2}{5}}$ .

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Step 5.1

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

$\frac{1}{x^{15 (\frac{2}{5})}}$

Step 5.2

Cancel the common factor of $5$ .

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Step 5.2.1

Factor $5$ out of $15$ .

$\frac{1}{x^{5 (3) \frac{2}{5}}}$

Step 5.2.2

Cancel the common factor.

$\frac{1}{x^{5 \cdot 3 \frac{2}{5}}}$

Step 5.2.3

Rewrite the expression.

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

Step 5.3

Multiply $3$ by $2$ .

$\frac{1}{x^{6}}$