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

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

Step 1

Move $x^{\frac{1}{2}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

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

Step 2

Multiply $x^{2}$ by $x^{- \frac{1}{2}}$ by adding the exponents.

Move $x^{- \frac{1}{2}}$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{4 x^{- \frac{1}{2} + 2}}$

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $2$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{1}{4 x^{\frac{- 1 + 4}{2}}}$

Add $- 1$ and $4$ .

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