Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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Step 3.1

Apply the product rule to $\frac{5}{y x^{2}}$ .

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

Step 3.2

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

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

Step 4

Raise $5$ to the power of $3$ .

$\frac{125}{y^{3} {(x^{2})}^{3}}$

Step 5

Multiply the exponents in ${(x^{2})}^{3}$ .

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Step 5.1

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

$\frac{125}{y^{3} x^{2 \cdot 3}}$

Step 5.2

Multiply $2$ by $3$ .

$\frac{125}{y^{3} x^{6}}$