Question

Need answer fast with all the steps included please

Answer 1

Answer:

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

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

Step-by-step 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

$(2x^3y^2)^3 = 2^3x^{3*3}y^{2*3}$

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