Question

Find the value of $x$ in terms of $y$ and $z$, if $xyz\ne 0$ and $30x^{-5}{y}^{12}{z}^{-8}=10x^{-6}{y}^5{z}^4$

• A. $\frac{z^{12}}{3y^7}$
• B. $\frac{3z^{12}}{y^7}$
• C. $\frac{3y^{12}}{z^7}$
• D. $\frac{3}{y^7{z}^4}$
• E. $\frac{3y^{17}}{z^4}$

Answer 1

The correct option is A $\frac{z^{12}}{3y^7}$

Given, $30x^{-5}{y}^{12}{z}^{-8}=10x^{-6}{y}^5{z}^4$

$\Rightarrow \frac{x^{-5}}{x^{-6}}=\frac{1}{3}\times \frac{y^5}{y^{12}}\frac{z^4}{z^{-8}}$
$\Rightarrow x^{-5+6}=\frac{1}{3}\times y^{5-12}{z}^{4+8}$
$\Rightarrow x=\frac{z^{12}}{3y^7}$