Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Combine.

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

Step 4

Multiply $1$ by $1$ .

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

Step 5

Change the sign of the exponent by rewriting the base as its reciprocal.

$5 y {(x y^{2})}^{2}$

Step 6

Apply the product rule to $x y^{2}$ .

$5 y (x^{2} {(y^{2})}^{2})$

Step 7

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

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Step 7.1

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

$5 y (x^{2} y^{2 \cdot 2})$

Step 7.2

Multiply $2$ by $2$ .

$5 y (x^{2} y^{4})$

Step 8

Multiply $y$ by $y^{4}$ by adding the exponents.

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Step 8.1

Move $y^{4}$ .

$5 (y^{4} y) x^{2}$

Step 8.2

Multiply $y^{4}$ by $y$ .

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Step 8.2.1

Raise $y$ to the power of $1$ .

$5 (y^{4} y^{1}) x^{2}$

Step 8.2.2

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

$5 y^{4 + 1} x^{2}$

Step 8.3

Add $4$ and $1$ .

$5 y^{5} x^{2}$