Simplify the Radical Expression (4x)^(1/2)

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

Step 1

Apply the product rule to $4 x$ .

$4^{\frac{1}{2}} x^{\frac{1}{2}}$

Step 2

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

${(2^{2})}^{\frac{1}{2}} x^{\frac{1}{2}}$

Step 3

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

$2^{2 (\frac{1}{2})} x^{\frac{1}{2}}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$2^{2 (\frac{1}{2})} x^{\frac{1}{2}}$

Rewrite the expression.

$2^{1} x^{\frac{1}{2}}$

Step 5

Evaluate the exponent.

$2 x^{\frac{1}{2}}$