Negative Exponents Notes

What is an Exponent? x4 = x ● x ● x ● x 26 = 2 ● 2 ● 2 ● 2 ● 2 ● 2 An exponent means that you multiply the base by itself that many times. For example x4 = x ● x ● x ● x 26 = 2 ● 2 ● 2 ● 2 ● 2 ● 2 = 64

Vocabulary Power – a number produced by raising a base to an exponent. (the term 27 is called a power.) Exponential form – a number written with a base and an exponent. (23) Exponent – the number that indicates how many times the base is used as a factor. (27) Base – when a number is being raised to a power, the number being used as a factor. (27)

Parts of a Power   2 4 exponent base Say: “2 to the fourth power” power

The Invisible Exponent When an expression does not have a visible exponent its exponent is understood to be 1.

Zero Exponent When anything, except 0, is raised to the zero power it is 1. For example ( if a ≠ 0) ( if x ≠ 0)

Negative exponents An exponent that is negative is not fully simplified. To simplify a negative exponent, take the reciprocal of the entire power. Leave the base and exponent the same. For example:

Negative Exponents The negative exponent basically flips the part with the negative exponent to the other half of the fraction.

You simplify

Mixed Practice