What is 3x^{1/6}*4x^{(-7)/6} ?

The solution to 3x^{1/6}*4x^{(-7)/6} is (12)/x

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simplify 3x^{1/6}*4x^{(-7)/6}

simplify

3 x^{\frac{1}{6}} \cdot 4 x^{\frac{- 7}{6}}

\frac{12}{x}

Solution steps

3 x^{\frac{1}{6}} \cdot 4 x^{\frac{- 7}{6}}

Multiply the numbers:

3 \cdot 4 = 12

= 12 x^{\frac{1}{6}} x^{\frac{- 7}{6}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

x^{\frac{1}{6}} x^{\frac{- 7}{6}} = x^{\frac{1}{6} + \frac{- 7}{6}}

= 12 x^{\frac{1}{6} + \frac{- 7}{6}}

\frac{1}{6} + \frac{- 7}{6} = - 1

= 12 x^{- 1}

Apply exponent rule:

a^{- 1} = \frac{1}{a}

x^{- 1} = \frac{1}{x}

= 12 \cdot \frac{1}{x}

Simplify

12 \cdot \frac{1}{x} : \frac{12}{x}

= \frac{12}{x}

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