Algebra Examples

${(\frac{6 x^{4}}{5 y})}^{- 2}$

Step 1

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

${(\frac{5 y}{6 x^{4}})}^{2}$

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 $\frac{5 y}{6 x^{4}}$ .

$\frac{{(5 y)}^{2}}{{(6 x^{4})}^{2}}$

Step 2.2

Apply the product rule to $5 y$ .

$\frac{5^{2} y^{2}}{{(6 x^{4})}^{2}}$

Step 2.3

Apply the product rule to $6 x^{4}$ .

$\frac{5^{2} y^{2}}{6^{2} {(x^{4})}^{2}}$

Step 3

Raise $5$ to the power of $2$ .

$\frac{25 y^{2}}{6^{2} {(x^{4})}^{2}}$

Step 4

Simplify the denominator.

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Step 4.1

Raise $6$ to the power of $2$ .

$\frac{25 y^{2}}{36 {(x^{4})}^{2}}$

Step 4.2

Multiply the exponents in ${(x^{4})}^{2}$ .

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Step 4.2.1

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

$\frac{25 y^{2}}{36 x^{4 \cdot 2}}$

Step 4.2.2

Multiply $4$ by $2$ .

$\frac{25 y^{2}}{36 x^{8}}$