Simplify each expression

1. √100m^6n^3

2. ^3√8x^12 / 27

√100m^6n^3

is the same as

√100 times √m^6 times √n^3

10 times m^(6/2) times √n^3

10 times m^3 times √n^3

10m^3 √n^3

i did it like this first so you can see how we can break up n^3 into (n^2)(n^1):

10m^3 √(n^2 times n^1)

10m^3 (√n^2 times √n)

10m^3 times n^(2/2) times √n

10m^3 times n^1 times √n

10m^3n √n






^3√[8x^12 / 27]

is the same as

^3√(8x^12) / ^3√27

[^3√8 times ^3√x^12] / 3

(2 times x^(12/3)) / 3

(2 times x^4) / 3

2x^4 / 3

can't simplify further.

10 * m^3 * n^(3/2) or 10 * m^3 * n√n
(2x^4)/3

The method for simplifying these monomials is fairly simple, when you know how to do them.
1) find the root of the numerical values
2) take each variable in alphabetical order, and just divide the root that is with each variable by the root of the radical. For example, in #1, m has a root of 6. The radical is a square root, which would mean the unwritten root number would be a 2. So, just divide the 6 by the 2 to get m^3.

If there is an odd number as a radical for the monomial under the sign, and an even number for a radical with the sign, then you will not have a perfect exponent. For example, for n^3 and the square root of 2, you would get n^(3/2) or n√n

10m^3n
2x^4/3