Question

The value of $(-5x^{2}y)\times (-\frac{2}{3}x{y}^{2}z)\times \left(\frac{8}{15}xy{z}^2\right)\times (-\frac{1}{4}z)$ is ______.

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

Answer 1

The correct option is A $-\frac{4}{9}{x}^4{y}^4{z}^4$

We have,

$(-5x^{2}y)\times (-\frac{2}{3}x{y}^{2}z)\times \left(\frac{8}{15}xy{z}^2\right)\times (-\frac{1}{4}z)=(-5\times (-\frac{2}{3})\times \frac{8}{15}\times (-\frac{1}{4}))\times (x^{2}y\times x{y}^{2}z\times xy{z}^2\times z)=(-\frac{2\times 2}{3\times 3})\times ((x^2\times x\times x)\times (y\times y^2\times y)\times (z\times z^2\times z))=(-\frac{4}{9})\times \left(x^4\right)\times \left(y^4\right)\times \left(z^4\right)=(-\frac{4}{9})\left(x^4\right)\left(y^4\right)\left(z^4\right)$

Answer is A