Simplify the expression using the properties of exponents. Expand any numerical portion of your answer and only include positive exponents.

Question

x⁷⋅x⁰

Answer 1

If definition of x⁰ considered a property, then x⁷ _* x⁰ = x⁷ _* 1 = x⁷

Or use x^m _* xⁿ = x^m+n, then x⁷ _* x⁰ = x⁷⁺⁰ = x⁷

Careful now! As always, the answer shall precisely match wording of the question. There is "expand", so x⁷ will not do as an answer!

Answer: x _* x _* x _* x _* x _* x _* x

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As a tutor, I always try to squeeze more out of any particular problem. In this case, I would mention the following.

1. On SAT Math, where questions are multiple choice, you will find the answer in the correct form.
2. On Algebra Regents, this problem can be open-ended and require reasoning. If you answered x⁷, you would get only partial credit (fewer points).

Answer 2

Using the properties of multiplying exponents, which is x^a * x^b = x^a+b, we can therefore say that x^{7 *} x⁰ = x⁷⁺⁰ = x⁷.