Question

Which shows the following expression after the negative exponents have been eliminated? xy^-6/x^-4y^2, x=/ 0, y=/ 0.

A. x^4/y^2x^6y^6
B. xx^4/y^2y^6
C. x^4/y^2xy^6
D. x^4y^2/xy^6

Answer 1

it should be option b

Answer 2

Answer:- B is the right answer,we get$\frac{x\cdot\ x^4}{y^2\cdot\ y^6}$ after negative exponents have been eliminated.

Explanation:-

Given expression :-   $\frac{xy^{-6}}{x^{-4}y^2},x\neq 0\ and\ y\neq0$

Rewriting the expression

$\frac{xy^{-6}}{x^{-4}y^2}=\frac{x}{x^{-4}}\times\frac{y^{-6}}{y^2}$

Now, to eliminate the negative exponents multiplying and dividing the expression by $x^{4}\ and \ y^{6}$ ,we get

$\frac{x}{x^{-4}}\times\frac{x^4}{x^4}\times\frac{y^{-6}}{y^2}\times\frac{y^6}{y^6}=\frac{x\cdot\ x^4}{x^{-4}\cdot\ x^4}\times\frac{y^{-6}\cdot\ y^6}{y^2\cdot\ y^6}$

we know that $a^n\times\ a^m=a^{n+m}$ [by exponents law]

$\Rightarrow\frac{x\cdot\ x^4}{x^{-4+4}}\times\frac{y^{-6+6}}{y^2\cdot\ y^6}=\frac{x\cdot\ x^4}{x^{0}}\times\frac{y^{0}}{y^2\cdot\ y^6}=\frac{x\cdot\ x^4}{y^2\cdot\ y^6}$ ....> which is option B.

Therefore B is the right answer.