Pre-Algebra Examples

${(\frac{2 y}{7 x^{3}})}^{- 2}$

Step 1

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

${(\frac{7 x^{3}}{2 y})}^{2}$

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 $\frac{7 x^{3}}{2 y}$ .

$\frac{{(7 x^{3})}^{2}}{{(2 y)}^{2}}$

Step 2.2

Apply the product rule to $7 x^{3}$ .

$\frac{7^{2} {(x^{3})}^{2}}{{(2 y)}^{2}}$

Step 2.3

Apply the product rule to $2 y$ .

$\frac{7^{2} {(x^{3})}^{2}}{2^{2} y^{2}}$

Step 3

Simplify the numerator.

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Step 3.1

Raise $7$ to the power of $2$ .

$\frac{49 {(x^{3})}^{2}}{2^{2} y^{2}}$

Step 3.2

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

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Step 3.2.1

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

$\frac{49 x^{3 \cdot 2}}{2^{2} y^{2}}$

Step 3.2.2

Multiply $3$ by $2$ .

$\frac{49 x^{6}}{2^{2} y^{2}}$

Step 4

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

$\frac{49 x^{6}}{4 y^{2}}$