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

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

Step 1

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

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

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

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

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

Multiply $\frac{3}{2}$ by $\frac{2}{2}$ .

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

Multiply $2$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $2$ .

$\frac{x^{\frac{- 1 + 6}{4}}}{x^{\frac{1}{3}}}$

Add $- 1$ and $6$ .

$\frac{x^{\frac{5}{4}}}{x^{\frac{1}{3}}}$

Step 2

Move $x^{\frac{1}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$x^{\frac{5}{4}} x^{- \frac{1}{3}}$

Step 3

Multiply $x^{\frac{5}{4}}$ by $x^{- \frac{1}{3}}$ by adding the exponents.

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

$x^{\frac{5}{4} - \frac{1}{3}}$

To write $\frac{5}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x^{\frac{5}{4} \cdot \frac{3}{3} - \frac{1}{3}}$

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x^{\frac{5}{4} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{4}{4}}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{4}$ by $\frac{3}{3}$ .

$x^{\frac{5 \cdot 3}{4 \cdot 3} - \frac{1}{3} \cdot \frac{4}{4}}$

Multiply $4$ by $3$ .

$x^{\frac{5 \cdot 3}{12} - \frac{1}{3} \cdot \frac{4}{4}}$

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$x^{\frac{5 \cdot 3}{12} - \frac{4}{3 \cdot 4}}$

Multiply $3$ by $4$ .

$x^{\frac{5 \cdot 3}{12} - \frac{4}{12}}$

Combine the numerators over the common denominator.

$x^{\frac{5 \cdot 3 - 4}{12}}$

Simplify the numerator.

Multiply $5$ by $3$ .

$x^{\frac{15 - 4}{12}}$

Subtract $4$ from $15$ .

$x^{\frac{11}{12}}$

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

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