What is (x^{-3})(3x^{-2})^{-1} ?

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

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simplify (x^{-3})(3x^{-2})^{-1}

simplify

(x^{- 3}) (3 x^{- 2})^{- 1}

\frac{1}{3 x}

Solution steps

(x^{- 3}) (3 x^{- 2})^{- 1}

Apply rule:

(a) = a

(x^{- 3}) = x^{- 3}

= x^{- 3} (3 x^{- 2})^{- 1}

Apply exponent rule:

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

x^{- 3} = \frac{1}{x ^{3}}

= \frac{1}{x ^{3}} (3 x^{- 2})^{- 1}

Simplify

(3 x^{- 2})^{- 1} : \frac{x ^{2}}{3}

= \frac{1}{x ^{3}} \cdot \frac{x ^{2}}{3}

Apply the fraction rule:

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

= \frac{1 \cdot x ^{2}}{x ^{3} \cdot 3}

Apply rule:

1 \cdot a = a

1 \cdot x^{2} = x^{2}

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

Simplify

\frac{x ^{2}}{x ^{3}} : \frac{1}{x}

= \frac{1}{x \cdot 3}

= \frac{1}{3 x}

- 3 x - 3 x

\frac{28}{21}

15 \times 2

\frac{2 x ^{3} - 8 x}{6 x ^{2} + 9 x - 6}

What is (x^{-3})(3x^{-2})^{-1} ?
The solution to (x^{-3})(3x^{-2})^{-1} is 1/(3x)