Simplify each expression. Assume all variables represent nonzero ...

Question

Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. -(2x^0y^4)^3

Accepted Answer

Hello everyone today. We're going to reduce the expression negative four P. To the zero Q. Two. The second raised to the fifth power. So the first thing I notice is that my negative is on the outside of my parentheses which means it just kind of stays there. It has nothing to do with the exponent of five. Now looking at the parentheses I know that I have a product. So multiplication. So each possible base within these parentheses needs get raised to the fifth power. So what that looks like is four needs to get raised to the 5th power. P. to the zero power gets raised to the 5th power And Q. to the second power also gets raised to the 5th power. So now that we've brought our exponent into the parentheses we can work on simplifying it again. My negative stays right out front of these parentheses because he has nothing to do with this. So four to the fifth power. It's gonna be P. to the 0 to the 5th power. Well when you raise the power to a power you multiply your exponents. So we end up with P. To the zero power because zero times five is zero. And then for Q when we raise the power to a power we're multiplying two times five which gives us 10. So we can simplify this a little bit more. I want you to recall that anything to the zero power is one. So that means that within our parentheses we can simplify a little bit more than we already had. Peter the zero is the same as one. So Now that I've written it down, I can multiply it in one times. 1024 is still 1024. So in my parentheses I end up with 1020 for Q to the 10th, but I still have that negative sign out front. So now is when I need to bring that in. So that's like multiplying by a negative one. So I end up with negative 1024 Q to the 10th. That is our simplified solution, which is answer choice C. See you next time.

Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. -(2x^0y^4)^3

Key Concepts

Exponents and Powers

Negative Exponents

Variable Representation

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