Basic Math Examples

${(- \frac{6 u^{3}}{4 v^{4}})}^{2}$

Step 1

Cancel the common factor of $6$ and $4$ .

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Step 1.1

Factor $2$ out of $6 u^{3}$ .

${(- \frac{2 (3 u^{3})}{4 v^{4}})}^{2}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $4 v^{4}$ .

${(- \frac{2 (3 u^{3})}{2 (2 v^{4})})}^{2}$

Step 1.2.2

Cancel the common factor.

${(- \frac{2 (3 u^{3})}{2 (2 v^{4})})}^{2}$

Step 1.2.3

Rewrite the expression.

${(- \frac{3 u^{3}}{2 v^{4}})}^{2}$

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 $- \frac{3 u^{3}}{2 v^{4}}$ .

${(- 1)}^{2} {(\frac{3 u^{3}}{2 v^{4}})}^{2}$

Step 2.2

Apply the product rule to $\frac{3 u^{3}}{2 v^{4}}$ .

${(- 1)}^{2} \frac{{(3 u^{3})}^{2}}{{(2 v^{4})}^{2}}$

Step 2.3

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

${(- 1)}^{2} \frac{3^{2} {(u^{3})}^{2}}{{(2 v^{4})}^{2}}$

Step 2.4

Apply the product rule to $2 v^{4}$ .

${(- 1)}^{2} \frac{3^{2} {(u^{3})}^{2}}{2^{2} {(v^{4})}^{2}}$

Step 3

Simplify the expression.

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Step 3.1

Raise $- 1$ to the power of $2$ .

$1 \frac{3^{2} {(u^{3})}^{2}}{2^{2} {(v^{4})}^{2}}$

Step 3.2

Multiply $\frac{3^{2} {(u^{3})}^{2}}{2^{2} {(v^{4})}^{2}}$ by $1$ .

$\frac{3^{2} {(u^{3})}^{2}}{2^{2} {(v^{4})}^{2}}$

Step 4

Simplify the numerator.

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Step 4.1

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

$\frac{9 {(u^{3})}^{2}}{2^{2} {(v^{4})}^{2}}$

Step 4.2

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

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Step 4.2.1

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

$\frac{9 u^{3 \cdot 2}}{2^{2} {(v^{4})}^{2}}$

Step 4.2.2

Multiply $3$ by $2$ .

$\frac{9 u^{6}}{2^{2} {(v^{4})}^{2}}$

Step 5

Simplify the denominator.

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Step 5.1

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

$\frac{9 u^{6}}{4 {(v^{4})}^{2}}$

Step 5.2

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

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Step 5.2.1

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

$\frac{9 u^{6}}{4 v^{4 \cdot 2}}$

Step 5.2.2

Multiply $4$ by $2$ .

$\frac{9 u^{6}}{4 v^{8}}$