Evaluate (4x^(5/4))/(2x^(1/2))

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

Step 1

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

$\frac{4 x^{\frac{5}{4}} x^{- \frac{1}{2}}}{2}$

Step 2

Multiply $x^{\frac{5}{4}}$ by $x^{- \frac{1}{2}}$ by adding the exponents.

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

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

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

$\frac{4 x^{- \frac{1}{2} + \frac{5}{4}}}{2}$

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{4 x^{- \frac{2}{2 \cdot 2} + \frac{5}{4}}}{2}$

Multiply $2$ by $2$ .

$\frac{4 x^{- \frac{2}{4} + \frac{5}{4}}}{2}$

Combine the numerators over the common denominator.

$\frac{4 x^{\frac{- 2 + 5}{4}}}{2}$

Add $- 2$ and $5$ .

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

Step 3

Factor $2$ out of $4 x^{\frac{3}{4}}$ .

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

Step 4

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $2 x^{\frac{3}{4}}$ by $1$ .

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