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

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

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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

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

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

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

Step 2

One to any power is one.

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

Step 3

Simplify the denominator.

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$\frac{1}{4 x}$