SOLUTION: Hi; I was wondering if you could help with this problem: -5y^4(y^5)^2/15y^7(y^2)^3

Question 324868: Hi; I was wondering if you could help with this problem:
-5y^4(y^5)^2/15y^7(y^2)^3
Answer by jessica43(140) (Show Source): You can put this solution on YOUR website!
To simplify this problem, you are going to use three basic exponent rules:
1. Whenever you multiply two terms with the same base, you can add the exponents:
(x^m)*(x^n) = x^(m+n)
2. Whenever you have an exponent expression that is raised to a power, you can multiply the exponent and power:
(x^m)^n = x^(m*n)
3. Whenever you divide two terms with the same base, you can subtract the exponents:
(x^m)/(x^n) = x^(m-n)
Now let's use these rules to solve this problem:
(-5y^4(y^5)^2)/(15y^7(y^2)^3)
((-5y^4)(y^10))/((15y^7)(y^6)) (I used rule 2: (y^5)^2 = y^10, (y^2)^3=y^6)
(-5y^14)/(15y^13) (I used rule 1: (y^4)(y^10)=y^14, (y^7)(y^6)=y^13)
-5y/15 (I used rule 3: (y^14)/(y^13)=y^(14-13)=y^1=y)
-y/3 (divided -5 by 15)
So your simplified equation is -y/3.

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