Basic Math Examples

$\frac{{(u^{2})}^{5}}{{(- 2 v^{4})}^{5}}$

Step 1

Multiply the exponents in ${(u^{2})}^{5}$ .

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Step 1.1

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

$\frac{u^{2 \cdot 5}}{{(- 2 v^{4})}^{5}}$

Step 1.2

Multiply $2$ by $5$ .

$\frac{u^{10}}{{(- 2 v^{4})}^{5}}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{u^{10}}{{(- 2)}^{5} {(v^{4})}^{5}}$

Step 2.2

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

$\frac{u^{10}}{- 32 {(v^{4})}^{5}}$

Step 2.3

Multiply the exponents in ${(v^{4})}^{5}$ .

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Step 2.3.1

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

$\frac{u^{10}}{- 32 v^{4 \cdot 5}}$

Step 2.3.2

Multiply $4$ by $5$ .

$\frac{u^{10}}{- 32 v^{20}}$

Step 3

Move the negative in front of the fraction.

$- \frac{u^{10}}{32 v^{20}}$