Pre-Algebra Examples

${(\frac{3 m^{3}}{5 n^{3}})}^{- 2}$

Step 1

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

${(\frac{5 n^{3}}{3 m^{3}})}^{2}$

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 $\frac{5 n^{3}}{3 m^{3}}$ .

$\frac{{(5 n^{3})}^{2}}{{(3 m^{3})}^{2}}$

Step 2.2

Apply the product rule to $5 n^{3}$ .

$\frac{5^{2} {(n^{3})}^{2}}{{(3 m^{3})}^{2}}$

Step 2.3

Apply the product rule to $3 m^{3}$ .

$\frac{5^{2} {(n^{3})}^{2}}{3^{2} {(m^{3})}^{2}}$

Step 3

Simplify the numerator.

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Step 3.1

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

$\frac{25 {(n^{3})}^{2}}{3^{2} {(m^{3})}^{2}}$

Step 3.2

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

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Step 3.2.1

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

$\frac{25 n^{3 \cdot 2}}{3^{2} {(m^{3})}^{2}}$

Step 3.2.2

Multiply $3$ by $2$ .

$\frac{25 n^{6}}{3^{2} {(m^{3})}^{2}}$

Step 4

Simplify the denominator.

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Step 4.1

Raise $3$ to the power of $2$ .

$\frac{25 n^{6}}{9 {(m^{3})}^{2}}$

Step 4.2

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

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Step 4.2.1

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

$\frac{25 n^{6}}{9 m^{3 \cdot 2}}$

Step 4.2.2

Multiply $3$ by $2$ .

$\frac{25 n^{6}}{9 m^{6}}$