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Examples of Exponential Expressions

Examples where people may disagree

Common Errors: Don't Go There!

Vocabulary

Equivalent

Equal to; the same as.

Exponent

An exponent tells how many times to multiply a number or term (the "base" ). The exponent is called a power. In 6^{3}, we read "Six to the third power," and 6 is multiplied 3 times: (6)(6)(6).

Like Bases

The base is the number or term that is raised to a power. Like bases have the same number or term raised to a power. The power (exponent) may be different.

Like Bases:
x^{3}, x^{4}
(ab)^{2}, (ab)^{y}
2x^{3}, x^{2}

NOT Like Bases:
y^{3}, x^{3}
(xy)^{2}, y^{2}
(2x)^{3}, x^{3}

Like Terms

Like terms are terms that have the exact same variables raised to the exact same exponents. A term is a number, variable, or the product of a number and variable(s). These are each terms: 4, x, 4x, 4x^{2}. In an expression, terms are separated by addition or subtraction operators (+,-).

Power

An exponent. A power tells how many times to multiply a number or term. In 6^{3}, we read "Six to the third power," and 6 is multiplied 3 times: (6)(6)(6).

Simplify

Reduce to lowest terms: eliminate parentheses, distribute, combine like terms, get rid of negative exponents.

This material is based upon work supported by the National Science Foundation (NSF) under Grant No. HRD-0726252. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.