Algebra Examples

${(x^{10})}^{\frac{1}{2}} \cdot x^{- 11}$

Step 1

Multiply the exponents in ${(x^{10})}^{\frac{1}{2}}$ .

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Step 1.1

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

$x^{10 (\frac{1}{2})} \cdot x^{- 11}$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $10$ .

$x^{2 (5) \frac{1}{2}} \cdot x^{- 11}$

Step 1.2.2

Cancel the common factor.

$x^{2 \cdot 5 \frac{1}{2}} \cdot x^{- 11}$

Step 1.2.3

Rewrite the expression.

$x^{5} \cdot x^{- 11}$

Step 2

Multiply $x^{5}$ by $x^{- 11}$ 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.

$x^{5 - 11}$

Step 2.2

Subtract $11$ from $5$ .

$x^{- 6}$

Step 3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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