Question

Which expression is equivalent to 3(sqrt)125x^6y^15z^3?

Answer 1

B. would be the correct choice here

Answer 2

Answer:

B. $5x^2 y^5 z$

Step-by-step explanation:

Given expression is,

$\sqrt[3]{125x^6y^{15}15z^3}$

$=\sqrt[3]{(5^3)(x^2)^3(y^5)^3(z)^3}$      ( $(a^{mn}=(a^m)^n$ )

$=\sqrt[3]{(5x^2 y^5 z)^3}$       ( $a^m.b^m=(ab)^m$ )

$=((5x^2 y^5 z)^3)^{\frac{1}{3}}$    ( $\sqrt[m]{a}=a^{\frac{1}{m}}$ )

$=(5x^2 y^5 z)^{3\times {\frac{1}{3}}$

$=(5x^2 y^5 z)^1$

$=5x^2 y^5 z$

Hence, option B is correct.