Question

The expression ${\left(x^{-2p}{y}^{3q}\right)}^6÷{\left(x^3{y}^{-1}\right)}^{-4p}$ after simplification becomes

• A. independent of x but not of y
• B. independent of y but not x
• C. independent of both x and y
• D. dependent of both x and y but independent of p and q

Answer 1

The correct option is A independent of x but not of y

${\left(x^{-2p}{y}^{3q}\right)}^6÷{\left(x^3{y}^{-1}\right)}^{-4p}$
${\left(x^{-2p}{y}^{3q}\right)}^6÷{\left(x^3{y}^{-1}\right)}^{-4p}$
$\Rightarrow {\left(\frac{y^{3q}}{x^{2p}}\right)}^6÷{\left(\frac{x^3}{y}\right)}^{-4p}$
$\Rightarrow {\left(\frac{y^{3q}}{x^{2p}}\right)}^6÷{\left(\frac{y}{x^3}\right)}^{4p}$
$\Rightarrow \frac{y^{18q}}{x^{12p}}÷\frac{y^{4p}}{x^{12p}}$
$\Rightarrow \frac{y^{18q}}{x^{12p}}\times \frac{x^{12p}}{y^{4p}}$
$\Rightarrow \frac{y^{18q}}{y^{4p}}$

Hence ,after simplification the result depended on the value of y .so it is independent of x but not of y