Simplify (16u^2)^(1/2)

${(16 u^{2})}^{\frac{1}{2}}$

Step 1

Simplify the expression.

Apply the product rule to $16 u^{2}$ .

$16^{\frac{1}{2}} {(u^{2})}^{\frac{1}{2}}$

Rewrite $16$ as $4^{2}$ .

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

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

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

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Simplify the expression.

Evaluate the exponent.

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

Multiply the exponents in ${(u^{2})}^{\frac{1}{2}}$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$4 u^{1}$

Step 4

Simplify.

$4 u$