Simplify the Radical Expression (5^(1/2)x^(1/4))^2

${(5^{\frac{1}{2}} x^{\frac{1}{4}})}^{2}$

Step 1

Apply the product rule to $5^{\frac{1}{2}} x^{\frac{1}{4}}$ .

${(5^{\frac{1}{2}})}^{2} {(x^{\frac{1}{4}})}^{2}$

Step 2

Multiply the exponents in ${(5^{\frac{1}{2}})}^{2}$ .

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

$5^{\frac{1}{2} \cdot 2} {(x^{\frac{1}{4}})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$5^{\frac{1}{2} \cdot 2} {(x^{\frac{1}{4}})}^{2}$

Rewrite the expression.

$5^{1} {(x^{\frac{1}{4}})}^{2}$

Step 3

Evaluate the exponent.

$5 {(x^{\frac{1}{4}})}^{2}$

Step 4

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

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

$5 x^{\frac{1}{4} \cdot 2}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$5 x^{\frac{1}{2 (2)} \cdot 2}$

Cancel the common factor.

$5 x^{\frac{1}{2 \cdot 2} \cdot 2}$

Rewrite the expression.

$5 x^{\frac{1}{2}}$