How do you multiply $2 x^{2} y^{5} {(9 x^{3} y)}^{- 3}$ $2x ^ { 2} y ^ { 5} ( 9x ^ { 3} y ) ^ { - 3}$ ?

Question

How do you multiply $2 x^{2} y^{5} {(9 x^{3} y)}^{- 3}$ $2x ^ { 2} y ^ { 5} ( 9x ^ { 3} y ) ^ { - 3}$ ?

1 Answer

Impact of this question

1073 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-22T01:00:22

See below.

Explanation:

Let's deal with the value inside the parenthesis first.

$2 x^{2} y^{5} {(9 x^{3} y)}^{- 3}$ $2x ^ { 2} y ^ { 5} ( 9x ^ { 3} y ) ^ { - 3}$

Remember that $x^{- a} = \frac{1}{x^{a}}$ $x^-a=1/x^a$

${(9 x^{3} y)}^{- 3} = 9^{- 3} x^{- 9} y^{- 3} = \frac{1}{729 x^{9} y^{3}}$ $( 9x ^ { 3} y ) ^ { - 3}=9^-3x^-9y^-3=1/(729x^9y^3)$

Combining,

$2 x^{2} y^{5} {(9 x^{3} y)}^{- 3} = 2 x^{2} y^{5} \cdot \frac{1}{729 x^{9} y^{3}}$ $2x ^ { 2} y ^ { 5} ( 9x ^ { 3} y ) ^ { - 3}=2x ^ { 2} y ^ { 5} *1/(729x^9y^3)$

$\frac{x^{a}}{x^{b}} = x^{a - b}$ $x^a/x^b=x^(a-b)$

So,

$2 x^{2} y^{5} \cdot \frac{1}{729 x^{9} y^{3}} = \frac{2 y^{2}}{729 x^{7}}$ $2x ^ { 2} y ^ { 5} *1/(729x^9y^3)=\frac(2y^2)(729x^7)$

Since $2$ $2$ and $9$ $9$ have no common multiples, this is our solution.

Science

Math

Humanities

... and beyond

How do you multiply $2 x^{2} y^{5} {(9 x^{3} y)}^{- 3}$ $2x ^ { 2} y ^ { 5} ( 9x ^ { 3} y ) ^ { - 3}$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you multiply 2x2y5(9x3y)−32x ^ { 2} y ^ { 5} ( 9x ^ { 3} y ) ^ { - 3}?

1 Answer

Explanation:

Related questions

Impact of this question

How do you multiply $2 x^{2} y^{5} {(9 x^{3} y)}^{- 3}$ $2x ^ { 2} y ^ { 5} ( 9x ^ { 3} y ) ^ { - 3}$ ?