# (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 | High School Teacher | (Level 1) Educator

Posted on

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, Grade 11 | (Level 1) Honors

Posted on

(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)