Answer:
[tex](8x^6) * (xy^2)^3 = 8x^9y^6[/tex]
[tex](2x^3y^2)^3 = 8x^9y^6[/tex]
Step-by-step explanation:
Given
[tex]8x^9y^6[/tex]
Required
Select 2 equivalent expressions
The equivalent expressions are (a) and (c) and the proof is as follows
(a)
[tex](8x^6) * (xy^2)^3[/tex]
Open brackets
[tex](8x^6) * (xy^2)^3 = 8x^6 * x^{1*3}y^{2*3}[/tex]
[tex](8x^6) * (xy^2)^3 = 8x^6 * x^3y^6[/tex]
Apply law of indices
[tex](8x^6) * (xy^2)^3 = 8x^{6+3}y^6[/tex]
[tex](8x^6) * (xy^2)^3 = 8x^9y^6[/tex]
(c)
[tex](2x^3y^2)^3[/tex]
Open brackets
[tex](2x^3y^2)^3 = 2^3x^{3*3}y^{2*3}[/tex]
[tex](2x^3y^2)^3 = 8x^9y^6[/tex]
