What is the "x" in a n expression of the form x^n?

Question

Algebra 1 Vocaubulary

Answer 1

The x is the base. The n is the exponent. If n is a positive integer, you multiply 1 by x n times. For example, 3⁴ = 1 * 3 * 3 * 3 * 3 = 81. If n is a negative integer, you divide 1 by x |n| times. For example, 5^-2 = 1 ÷ 5 ÷ 5 = 1/25 or 0.04. The bars around the n, in the second case, denote absolute value or magnitude, which means "How far is n from 0?" The absolute value of 2 is 2, and the absolute value of -2 is 2, because both are two units away from 0. Finally, if n is 0, and x is not 0, then xⁿ = 1, because you are not doing anything to the 1 you are starting out with.

 

Why is 0⁰ undefined, you might ask? 0ⁿ, when n > 0, is 0. x⁰, when x ≠ 0, is 1. If you put the two cases together, as 0⁰, will your answer be 0 or 1? You cannot determine the answer, so the result is an indeterminate form, which is basically just a kind of undefined.

Answer 2

5^3     5 is the base, 3 is the exponent 

7x^2 7 is the coefficient, x is the base, 2 is the exponent