Simplify this problem?

Question

5y^3(y^5)^2 / 10y^5(y^2)^6

Answer 1

Review the rules for exponents and follow the order of operations.

(a^m)^n = a^(mn)
Ex. (y^2)^6 = y^(12)

(a^n)(a^m) = a^(m+n)

(a^m) / (a^n) = a^(m-n)
Ex. y^13 / y^17 = y^(-4)

a^(-n) = 1/(a^n)
Ex. y(-4) = 1/(y^4)

1/[a^(-n)] = a^n

Answer 2

Laws of Exponents
http://oakroadsystems.com/math/expolaws.htm

5y^3(y^5)^2 / 10y^5(y^2)^6 = 1/(2y^4) Simplified

First Part / Second Part
break it down

First Part

5y^3(y^5)^2
5y^3
(y^5)^2 = y^10 multiply Exponents

5y^3*y^10 = 5y^13 add Exponents

Second Part

10y^5(y^2)^6
10y^5
(y^2)^6 = y^12 multiply Exponents

10y^5*y^12 = 10y^17 add Exponents

Put it back together:

(5y^13)/(10y^17) = 1/(2y^4) Simplified

Answer 3

5 y^3(y^5)2/10y^5(y^2)^6 =
= 10 y^8/10y^5(y^12) =
= 10y^8/10y^17 =
= y^8/y^17 =
= 1/y^9

or:

10y^3.y^5/10y^5.y^12 =
= y^3/y^12 =
= 1/y^9

Answer 4

5y^3(y^5)^2 / 10y^5(y^2)^6
= 1 / (2y^4)

this could also be written
=0.5 * 1/y^4
= 0.5 * y^(-4)

Answer 5

1. y^13 / 2y^17

2. 1 / 2y^4 or y^-4/2

Answer 6

Do your own homework. Simple.