Algebra Examples

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

Step 1

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

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

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.1

Apply the product rule to $\frac{1}{y^{5} x}$ .

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

Step 2.2

Apply the product rule to $y^{5} x$ .

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

Step 3

One to any power is one.

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

Step 4

Multiply the exponents in ${(y^{5})}^{2}$ .

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Step 4.1

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

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

Step 4.2

Multiply $5$ by $2$ .

$\frac{1}{y^{10} x^{2}}$