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Simplify the following expression as far as possible: ( 2 xy 2 ) 3 ÷ 3 x 2 y 3 × 9 x 3 y 2

Siphe  Aug 15, 2017
 #1
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(If you wanted us to do four questions, please put them all in one question rather than serving all of them in quick succession.)

Input:( 2 xy 2 ) 3 ÷ 3 x 2 y 3 × 9 x 3 y 2

Intepretation: \(\frac{\left(2xy^2\right)^3}{3x^2y^3}\cdot 9x^3y^2\)

Simplification:

\(=\frac{\left(2xy^2\right)^3}{y}\cdot 3x\)

Extract 2 out of the parenthese:

\(=\frac{8\left(xy^2\right)^3}{y}\cdot 3x\)

Continue Simplification:

\(=\frac{8(x^3y^6)}{y}\cdot 3x\)

\(=8x^3y^5\cdot 3x\)

\(=24x^4y^5\)

Q.E.D.

Jeffes02  Aug 15, 2017
 #2
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\((2xy^2)^3\div(3x^2y^3)\times (9x^3y^2)\\ =(2^3\div 3\times 9)\times (x^3\div x^2 \times x^3)\times ((y^2)^3\div y^3\times y^2)\\ =24x^4y^5\)

MaxWong  Aug 15, 2017

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