SOLUTION: need to simplify the following (-5x^5y^6)^3

Question 237878: need to simplify the following
(-5x^5y^6)^3
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Until you get comfortable with exponents and the rules for working with them, one way to do problems like this is to rewrite the expression without the exponents:

Now we can use the Commutative and Associative Properties to rearrange and regroup the "like" factors:

And then we simplify each group by multiplying out the numbers and rewriting the variables using exponents. Since -5*-5*-5 = -125 we get:

A shorter way, that you will learn eventually, is to use the properties of exponents effectively. Since is a single term (you have to have additions and/or subtractions to have more than one term), you can use the property:

I call this a pseudo-distributive property because it looks similar to the Distributive Property (but it's not). The property lets us "distribute" or apply the exponent outside the parentheses to each factor of the one term expression inside the parentheses. Using this on your expression we get:

We can multiply out the -5, and we use another property of exponents, , on the variables we get:

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