Simplify the Radical Expression (100x^4)^(1/2)

${(100 x^{4})}^{\frac{1}{2}}$

Step 1

Apply the product rule to $100 x^{4}$ .

$100^{\frac{1}{2}} {(x^{4})}^{\frac{1}{2}}$

Step 2

Rewrite $100$ as $10^{2}$ .

${(10^{2})}^{\frac{1}{2}} {(x^{4})}^{\frac{1}{2}}$

Step 3

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

$10^{2 (\frac{1}{2})} {(x^{4})}^{\frac{1}{2}}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$10^{2 (\frac{1}{2})} {(x^{4})}^{\frac{1}{2}}$

Rewrite the expression.

$10^{1} {(x^{4})}^{\frac{1}{2}}$

Step 5

Evaluate the exponent.

$10 {(x^{4})}^{\frac{1}{2}}$

Step 6

Multiply the exponents in ${(x^{4})}^{\frac{1}{2}}$ .

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

$10 x^{4 (\frac{1}{2})}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$10 x^{2 (2) \frac{1}{2}}$

Cancel the common factor.

$10 x^{2 \cdot 2 \frac{1}{2}}$

Rewrite the expression.

$10 x^{2}$