Simplify (14xy^(1/3))/(2x^(3/4)z^-6)

$\frac{14 x y^{\frac{1}{3}}}{2 x^{\frac{3}{4}} z^{- 6}}$

Step 1

Move $x^{\frac{3}{4}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$\frac{14 x y^{\frac{1}{3}} x^{- \frac{3}{4}}}{2 z^{- 6}}$

Step 2

Move $z^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{14 x y^{\frac{1}{3}} x^{- \frac{3}{4}} z^{6}}{2}$

Step 3

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

Move $x^{- \frac{3}{4}}$ .

$\frac{14 (x^{- \frac{3}{4}} x) y^{\frac{1}{3}} z^{6}}{2}$

Multiply $x^{- \frac{3}{4}}$ by $x$ .

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

$\frac{14 (x^{- \frac{3}{4}} x^{1}) y^{\frac{1}{3}} z^{6}}{2}$

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

$\frac{14 x^{- \frac{3}{4} + 1} y^{\frac{1}{3}} z^{6}}{2}$

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

$\frac{14 x^{- \frac{3}{4} + \frac{4}{4}} y^{\frac{1}{3}} z^{6}}{2}$

Combine the numerators over the common denominator.

$\frac{14 x^{\frac{- 3 + 4}{4}} y^{\frac{1}{3}} z^{6}}{2}$

Add $- 3$ and $4$ .

$\frac{14 x^{\frac{1}{4}} y^{\frac{1}{3}} z^{6}}{2}$

Step 4

Factor $2$ out of $14 x^{\frac{1}{4}} y^{\frac{1}{3}} z^{6}$ .

$\frac{2 (7 x^{\frac{1}{4}} y^{\frac{1}{3}} z^{6})}{2}$

Step 5

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 (7 x^{\frac{1}{4}} y^{\frac{1}{3}} z^{6})}{2 (1)}$

Cancel the common factor.

$\frac{2 (7 x^{\frac{1}{4}} y^{\frac{1}{3}} z^{6})}{2 \cdot 1}$

Rewrite the expression.

$\frac{7 x^{\frac{1}{4}} y^{\frac{1}{3}} z^{6}}{1}$

Divide $7 x^{\frac{1}{4}} y^{\frac{1}{3}} z^{6}$ by $1$ .

$7 x^{\frac{1}{4}} y^{\frac{1}{3}} z^{6}$

Step 6

Reorder factors in $7 x^{\frac{1}{4}} y^{\frac{1}{3}} z^{6}$ .

$7 z^{6} x^{\frac{1}{4}} y^{\frac{1}{3}}$