Question

For all $xyz\ne 0$, simplify $\frac{6x^2{y}^{12}{z}^6}{(2x^{2}yz{)}^3}$.

• A. $\frac{y^4{z}^2}{x^3}$
• B. $\frac{y^9{z}^4}{x^4}$
• C. $\frac{y^9{z}^3}{2x^3}$
• D. $\frac{3y^4{z}^2}{4x^3}$
• E. $\frac{3y^9{z}^3}{4x^4}$

Answer 1

The correct option is E $\frac{3y^9{z}^3}{4x^4}$

The value of $\frac{6x^2{y}^{12}{z}^6}{(2x^{2}yz{)}^3}$

$=$ $\frac{6x^2{y}^{12}{z}^6}{8x^6{y}^3{z}^3}$

$=$ $\frac{3}{4}{x}^{2-6}{y}^{12-3}{z}^{6-3}$

$=$ $\frac{3}{4}{x}^{-4}{y}^9{z}^3$

$=$ $\frac{3y^9{z}^3}{4x^4}$