which of the following simplify to the same expression? select all that apply. a) $(x^{2}y)^{2}$ b)…

which of the following simplify to the same expression? select all that apply. a) $(x^{2}y)^{2}$ b) $(x^{3})^{2}y^{6}$ c) $(x^{3})^{2}(y^{2})^{4}$ d) $(x^{3}y^{4})^{2}$ e) $x^{6}(y^{4})^{2}$

which of the following simplify to the same expression? select all that apply. a) $(x^{2}y)^{2}$ b) $(x^{3})^{2}y^{6}$ c) $(x^{3})^{2}(y^{2})^{4}$ d) $(x^{3}y^{4})^{2}$ e) $x^{6}(y^{4})^{2}$

Answer

Explanation:

Step1: Simplify option A

Using the power - of - a - product rule $(ab)^n=a^n b^n$ and power - of - a - power rule $(a^m)^n=a^{mn}$, we have $(x^{2}y)^{2}=(x^{2})^{2}y^{2}=x^{4}y^{2}$.

Step2: Simplify option B

$(x^{3})^{2}y^{6}=x^{6}y^{6}$ (by power - of - a - power rule $(a^m)^n=a^{mn}$).

Step3: Simplify option C

$(x^{3})^{2}(y^{2})^{4}=x^{6}y^{8}$ (using power - of - a - power rule for both $x$ and $y$ terms: $(a^m)^n=a^{mn}$).

Step4: Simplify option D

$(x^{3}y^{4})^{2}=(x^{3})^{2}(y^{4})^{2}=x^{6}y^{8}$ (by power - of - a - product rule $(ab)^n=a^n b^n$ and power - of - a - power rule $(a^m)^n=a^{mn}$).

Step5: Simplify option E

$x^{6}(y^{4})^{2}=x^{6}y^{8}$ (using power - of - a - power rule $(a^m)^n=a^{mn}$).

Answer:

C. $(x^{3})^{2}(y^{2})^{4}$, D. $(x^{3}y^{4})^{2}$, E. $x^{6}(y^{4})^{2}$