SOLUTION: Simplify. Assume that all variables represent positive numbers. <a href="http://photobucket.com" target="_blank"><img src="http://i83.photobucket.com/albums/j300/q43000gt/8q5g2

Question 47843: Simplify. Assume that all variables represent positive numbers.

Answer by BGluvsmath(64) (Show Source): You can put this solution on YOUR website!
By the rules of exponents, when you take a root of a variable to a certain power, you subtract the root from the exponent of the variable. As an example, the cube root of m^7 equals m^(7-3), or m^4. Keeping that in mind,:
5(cube root of (m^7p^5))-2m^2p(cube root of (mp^2))
5(m^(7-3)p^(5-3))-2m^2p(m^-3p^(2-3))
The first part simplifies to 5m^4p^2-2m^2p
Given the rule of negative exponents (x^-1=1/x), the rest simplifies to 1/m^3p
Complete expression to this point: 5m^4p^2-(2m^2p/m^3p)
2m^2p/m^3p simplifies to 2/m because the p's cancel out and the m's simplify to 1/m
So now we have 5m^4p^2-2/m, which is equivalent to 5m^5p^2/m-2/m when we give each term the same denominator, required for adding and subtracting fractions.
This simplifies to (5m^5p^2-2)/m. No further simplification is possible.
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