What is (6x^24y^{-5})(1/3 x^{-3}y^2) ?

The solution to (6x^24y^{-5})(1/3 x^{-3}y^2) is 8/(y^3x)

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simplify (6x^24y^{-5})(1/3 x^{-3}y^2)

simplify

(6 x^{2} 4 y^{- 5}) (\frac{1}{3} x^{- 3} y^{2})

\frac{8}{y ^{3} x}

Solution steps

(6 x^{2} \cdot 4 y^{- 5}) (\frac{1}{3} x^{- 3} y^{2})

Simplify

6 x^{2} \cdot 4 y^{- 5} : \frac{24 x ^{2}}{y ^{5}}

= \frac{24 x ^{2}}{y ^{5}} \cdot \frac{1}{3} x^{- 3} y^{2}

Apply exponent rule:

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

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

= \frac{24 x ^{2}}{y ^{5}} \cdot \frac{1}{3} \cdot \frac{1}{x ^{3}} y^{2}

Apply the fraction rule:

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

= \frac{24 x ^{2} \cdot 1 \cdot 1 \cdot y ^{2}}{y ^{5} \cdot 3 x ^{3}}

Multiply the numbers:

24 \cdot 1 \cdot 1 = 24

= \frac{24 x ^{2} y ^{2}}{y ^{5} \cdot 3 x ^{3}}

Factor the number:

24 = 3 \cdot 8

= \frac{3 \cdot 8 x ^{2} y ^{2}}{y ^{5} \cdot 3 x ^{3}}

Cancel the common factor:

3

= \frac{8 x ^{2} y ^{2}}{y ^{5} x ^{3}}

Simplify

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

= \frac{8 y ^{2}}{y ^{5} x}

Simplify

\frac{y ^{2}}{y ^{5}} : \frac{1}{y ^{3}}

= \frac{8}{y ^{3} x}

2 < 3 a < 8

4 x^{2} + 4 x + 4

\frac{5 x + 3 y}{2 x ^{2} y} - \frac{3 x + 4 y}{x y ^{2}}

16 t^{2} + 80 t + 32 = 0

- 2 x^{2} + 8

What is (6x^24y^{-5})(1/3 x^{-3}y^2) ?
The solution to (6x^24y^{-5})(1/3 x^{-3}y^2) is 8/(y^3x)