8 1 EXPONENTS Base 3 4 Exponent An

8. 1 EXPONENTS

Base 3 4 Exponent An exponent tells how many times a number is multiplied by itself. 4 3 = (3) (3)

How to Simplify 4 3 = 3 x 3 x 3 9 27 81

4 4 -2 (-2) not the same 4 -2 = -(2 • 2 • 2)= -16 4 (-2) =(-2)(-2) = 16

3 4 2 = 2 3 2 4 = 9 16

Evaluate 3 2 X when X = 4 3 2(4) = 2(64)= 128 not the same 3 as 8

Evaluate 2 (X Y) 2 (3 • -2) 2 (-6) 36 when X= 3 Y= -2

2 4 (X ) (2+4) X 6 X = = 6 (X X)(XXXX) = X -To multiply with the same base, ADD the exponents.

2 2 4 2 (2+4) 2 = = (2 • 2) (2 • 2 • 2) There are 6 twos. 6 2

To Divide with the same base, subtract exponents. aaaaaaa

To Divide with the same base, subtract exponents 5 X = X 2 X 5 -2 3 =X

To Divide with the same base, subtract exponents 3 10 (10)(10) 1 = = 10 2 10 (10) 1000 = 10 100

When the exponent is zero, the result is one.

Simplify 0 - y = -1 0 12 = 1

2 b 7 b • 9 b = add exp p 4 2 p = 2 p 3 b 2 = 9 b 5 _1__ reduce fraction 3 3 b subt exp

put like terms together

new rule exponent outside ( ) multiply 2 3 6 (2 ) = 2 exponents 2 2 2 6 (2 ) = 2

Exponents outside ( ) are used on EACH TERM inside ( ). 3 2 (2 X Y ) 6 2 = 4 X Y

Try these 2 5 (5 ) = 10 5 2 (4 X) = 2 16 X 3 3 3 = 3 X = 27 3 X

Thought for the day The mathematical rules of universe are visible to men in the form of beauty.