Simplify (4x)/(9x^(1/2))

$\frac{4 x}{9 x^{\frac{1}{2}}}$

Step 1

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

$\frac{4 x \cdot x^{- \frac{1}{2}}}{9}$

Step 2

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

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

$\frac{4 (x^{- \frac{1}{2}} x)}{9}$

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

Raise $x$ to the power of $1$ .

$\frac{4 (x^{- \frac{1}{2}} x^{1})}{9}$

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

$\frac{4 x^{- \frac{1}{2} + 1}}{9}$

Write $1$ as a fraction with a common denominator.

$\frac{4 x^{- \frac{1}{2} + \frac{2}{2}}}{9}$

Combine the numerators over the common denominator.

$\frac{4 x^{\frac{- 1 + 2}{2}}}{9}$

Add $- 1$ and $2$ .

$\frac{4 x^{\frac{1}{2}}}{9}$