Unit 4 - Objective 1 - Simplifying Expressions with Integral Exponents
Quick Review

Exponents are operations to do:

32 means multiply 3 by itself 2 times = (3) (3) = 9

3-1 means to take the reciprocal of 3 = 1/3




Example 1



Example 2

Any non-zero number raised to the zero power equals 1.

  1. a0 = 1 for a does not equal 0.

  2. 30 = 1

  1. (9x)0 = 1

  2. 9x0 = 9 . x0 = 9 . 1 = 9


Example 3
When multiplying the same base: keep the base and add the exponents.
aman = am+n

1. a7a5 = a7+5 = a12

2. a9a-3 = a9+(-3) = a6

3. x5x-7 = x5+(-7) = x-2 = 1 over x squared



Example 4

When dividing the same base: keep the base and subtract the exponents. This is the same as reducing a fraction.




Example 5
When raising a power to a power: multiply the exponents.
(am)n = amn

1. (a5)3 = a(5) (3) = a15

2.



Example 6
Exponents distribute across multiplication and division
(NOT across addition and subtraction).

(ab)n = anbn


3. (x + 3)2 = (x + 3) (x + 3)

= x2 + 3x + 3x + 9

= x2 + 6x + 9



Example 7

A negative exponent represents a reciprocal. Remove a negative in the exponent by taking the reciprocal. In a product or quotient, that means moving the base and exponent from the numerator to the denominator or vice-versa, changing the sign in the exponent.




Example 8

Exponents only apply to a single character unless there are parentheses.




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