Question

Which expression is equivalent to 10x^6y^12/-5x^-2y^-6?

Answer 1

$\cfrac{10x^6y^{12}}{-5x^{-2}y^{-6}} =-2x^{6-(-2)}y^{12-(-6)}=-2x^{6+2}y^{12+6}=-2x^8y^{18}$

Answer: B)-2x^8y^18

Answer 2

Answer: Option 'B' is correct.

Step-by-step explanation:

Since we have given that

$\frac{10x^6y^{12}}{-5x^-2y^-6}$

We will use two rules :

$a^m\times a^n=a^{m+n}\\\\and,\\\\a^m\div a^n=a^{m-n}$

So, it will become,

$\frac{10x^6y^{12}}{-5x^{-2}y^{-6}}\\\\\frac{10}{-5}\times \frac{x^6}{x^{-2}}\times \frac{y^{12}}{y^{-6}}\\\\=-2\times x^{6-(-2)}\times y^{12-(-6)}\\\\=-2x^{6+2}\times y^{12+6}\\\\=-2x^{8}y^{18}$

Hence, Option 'B' is correct.