Exponents An exponent is the number of times the base is multiplied by itself. Example 27 can also be written as 3 This means 3 X 3 X 3 3

Substituting variables for numbers We can also use variables such as X and Y when using exponents. We can define X and Y as integers. For example: 3 = 3 X 3 X 3 = 27 SO: X = (X)(X)(X) 3 3

Variable A variable is a symbol for a number we don’t know yet like X or Y.

Integers Integers include zero, positive and negative numbers. They do not include fractions.

Laws of Exponents N X = (X)(X)…..(X) (N factors of X) X = 1 (if X = 0) X X = X -n n 1/N N

Practice Write 11 as multiplication. 3 Write 11 as multiplication. Write u as a fraction using only positive exponents. What is the value of 100 ? Evaluate -5 and (-5) -7 1/2 -2 -2

Solutions 11 X 11 X 11 = 1331 1 u 10 25 7

Multiplying Exponents Same base (X ) (X) = X Be careful I can add the exponents, because X is the base both time. If I had X and Y I could only combine in the exponents were the same. 5 6 11

Differences Math is a language 3 3 3 (4x) means (4 ) (X ) 4x means 4 (X)(X)(X) 3

Dividing Exponents Step 1: X X = Step 2: X = 1 X Step 3: (X ) (X ) = X 8 6 Step 1: X X = Step 2: X = 1 X Step 3: (X ) (X ) = X 8 6 2 8 -6

Dividing Exponents 8 6 Step 1: X X = Step 2: (XX) (XXXXXX) (XXXXXX) STEP 3: (XX) (XXXXXX) (XXXXXX) Step 3: (XX) = X 2

x Anything divided by itself is 1. X to the zero power is 1. Anything divided by itself is 1. X to the zero power is 1. Example X / X = (X ) (X ) = 1 This works in all cases except for if X is equal to zero. 3 -3 3 3