What is (6x^3)(3xy)^{-1} ?

The solution to (6x^3)(3xy)^{-1} is (2x^2)/y

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simplify (6x^3)(3xy)^{-1}

simplify

(6 x^{3}) (3 x y)^{- 1}

\frac{2 x ^{2}}{y}

Solution steps

(6 x^{3}) (3 x y)^{- 1}

Apply exponent rule:

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

(3 x y)^{- 1} = \frac{1}{3 x y}

= 6 x^{3} \frac{1}{3 x y}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{6 x ^{3} \cdot 1}{3 x y}

Multiply the numbers:

6 \cdot 1 = 6

= \frac{6 x ^{3}}{3 x y}

Factor the number:

6 = 3 \cdot 2

= \frac{3 \cdot 2 x ^{3}}{3 x y}

Cancel the common factor:

3

= \frac{2 x ^{3}}{x y}

Simplify

\frac{x ^{3}}{x} : x^{2}

= \frac{2 x ^{2}}{y}

\frac{x}{9 x ^{2} - 1} > 0

(x - 2) (x + 9) = - 10

(x - 1) (x + 7) \leq 0

\frac{16 y x ^{4}}{9 x ^{8} y ^{2}}

(7 + 10) (7 - 10)