Basic Math Examples

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

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to $4 u$ .

$4^{\frac{3}{2}} u^{\frac{3}{2}}$

Step 1.2

Rewrite $4$ as $2^{2}$ .

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

Step 1.3

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

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

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

$2^{3} u^{\frac{3}{2}}$

Step 3

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

$8 u^{\frac{3}{2}}$