# (X^10)(Y^-1)/(X^-5)(Y^5)I tried dividing coeficcients and then substracting exponents. It gave me (X^15)(Y^-6). This is almost right, but the answer booklet says it should be X^15/Y^6 and i'm not...

(X^10)(Y^-1)/(X^-5)(Y^5)

I tried dividing coeficcients and then substracting exponents. It gave me (X^15)(Y^-6). This is almost right, but the answer booklet says it should be X^15/Y^6 and i'm not sure why.

beckden | Certified Educator

When dealing with exponents, the convention is that an expression is not simplified if it has negative exponents in it.

So since `a^(-b) = 1/a^b`

The answer you got `x^15y^(-6)` is not fully simplifed because it has a negative exponent.  Since `y^(-6) = 1/y^6` the equivalent expression `x^15/y^6` is the correct answer because it does not have any negative exponents.

I hope that helps.

utkr940 | Student

(x^10)(y^-1)/(x^-5)(y^5)

This expression can be written as

(x^10)(x^5)/(y^1)(y^5)

= x^(10+5)/y^(1+5)

=(x^15)/(y^6)=(x^15)(y^-6)

amandam4l | Student

The parentheses are there just to indicate to do that part of the equation first.  Also the division is like a fraction and since you got a (y^-6) it would go onto the bottom of the fraction.  So you did get the right answer you did it correctly.  You just have to look up those rules and remeber them so you don't fail a test just cause you changed your answer. Don't worry I may be young but I am taking colledge math and science classes so I know.  I got it out of my head so look it up if you don't believe me...