Simplify (25x^(3/4))^(1/2)

${(25 x^{\frac{3}{4}})}^{\frac{1}{2}}$

Step 1

Simplify the expression.

Apply the product rule to $25 x^{\frac{3}{4}}$ .

$25^{\frac{1}{2}} {(x^{\frac{3}{4}})}^{\frac{1}{2}}$

Rewrite $25$ as $5^{2}$ .

${(5^{2})}^{\frac{1}{2}} {(x^{\frac{3}{4}})}^{\frac{1}{2}}$

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

$5^{2 (\frac{1}{2})} {(x^{\frac{3}{4}})}^{\frac{1}{2}}$

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

$5^{2 (\frac{1}{2})} {(x^{\frac{3}{4}})}^{\frac{1}{2}}$

Rewrite the expression.

$5^{1} {(x^{\frac{3}{4}})}^{\frac{1}{2}}$

Step 3

Evaluate the exponent.

$5 {(x^{\frac{3}{4}})}^{\frac{1}{2}}$

Step 4

Multiply the exponents in ${(x^{\frac{3}{4}})}^{\frac{1}{2}}$ .

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

$5 x^{\frac{3}{4} \cdot \frac{1}{2}}$

Multiply $\frac{3}{4} \cdot \frac{1}{2}$ .

Multiply $\frac{3}{4}$ by $\frac{1}{2}$ .

$5 x^{\frac{3}{4 \cdot 2}}$

Multiply $4$ by $2$ .

$5 x^{\frac{3}{8}}$