Question

Need answer fast with all the steps included please

Answer 1

`(8x^6) * (xy^2)^3 = 8x^9y^6`

`(2x^3y^2)^3 = 8x^9y^6`

Explanation:

Given

`8x^9y^6`

Required

Select 2 equivalent expressions

The equivalent expressions are (a) and (c) and the proof is as follows

(a)

`(8x^6) * (xy^2)^3`

Open brackets

`(8x^6) * (xy^2)^3 = 8x^6 * x^(1*3)y^(2*3)`

`(8x^6) * (xy^2)^3 = 8x^6 * x^3y^6`

Apply law of indices

`(8x^6) * (xy^2)^3 = 8x^(6+3)y^6`

`(8x^6) * (xy^2)^3 = 8x^9y^6`

(c)

`(2x^3y^2)^3`

Open brackets

`(2x^3y^2)^3 = 2^3x^(3*3)y^(2*3)`

`(2x^3y^2)^3 = 8x^9y^6`