Simplify ((3x^(1/2))/15)^2

${(\frac{3 x^{\frac{1}{2}}}{15})}^{2}$

Step 1

Factor $3$ out of $3 x^{\frac{1}{2}}$ .

${(\frac{3 (x^{\frac{1}{2}})}{15})}^{2}$

Step 2

Cancel the common factors.

Factor $3$ out of $15$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

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

Step 4

Simplify the numerator.

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Step 5

Raise $5$ to the power of $2$ .

$\frac{x}{25}$