Page 92 - MarceAlgebra Demystified

CHAPTER 5

Exponents and Roots

The expression 4x is shorthand for x þ x þ x þ x, that is x added to itself
4
four times. Likewise x is shorthand for x x x x—x multiplied by itself
4
four times. In x , x is called the base and 4 is the power or exponent. We say
‘‘x to the fourth power’’ or simply ‘‘x to the fourth.’’ There are many useful
exponent properties. For the rest of the chapter, a is a nonzero number.
n m m+n
Property 1 a a ¼ a
When multiplying two powers whose bases are the same, add the exponents.

Examples

4
3
9
3
2 2 ¼ð2 2 2Þð2 2 2 2Þ¼ 2 7 x x ¼ x 12
a m m n
Property 2 ¼ a
a n
When dividing two powers whose bases are the same, subtract the denomi-
nator’s power from the numerator’s power.

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