Simplify (x^(1/2)*x^(-3/4))/(x^(1/4))

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

Step 1

Multiply $x^{\frac{1}{2}}$ by $x^{- \frac{3}{4}}$ by adding the exponents.

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

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

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

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

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

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

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

Multiply $2$ by $2$ .

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

Combine the numerators over the common denominator.

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

Subtract $3$ from $2$ .

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

Move the negative in front of the fraction.

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

Step 2

Move $x^{- \frac{1}{4}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 3

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

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

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

Combine the numerators over the common denominator.

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

Add $1$ and $1$ .

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

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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