Question

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

A) -50x^8y^18
B)-2x^8y^18
C) -2x^12y^72
D)5x^8y^18

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.

Explanation:

Since we have given that

`(10x^6y^(12))/(-5x^-2y^-6)`

We will use two rules :

`a^m* a^n=a^(m+n)\\\\and,\\\\a^m/ a^n=a^(m-n)`

So, it will become,

`(10x^6y^(12))/(-5x^(-2)y^(-6))\\\\(10)/(-5)* (x^6)/(x^(-2))* (y^(12))/(y^(-6))\\\\=-2* x^(6-(-2))* y^(12-(-6))\\\\=-2x^(6+2)* y^(12+6)\\\\=-2x^(8)y^(18)`

Hence, Option 'B' is correct.