exponents and powers

a number written asa base number with an exponent BASE EXPONENT

LIKE THIS:

2 SAY 2 TO THE 5th POWER

THE REPEATED FRACTION IN A MULTIPLICATON PROBLEM

BASE = POWER

FACTOR * FACTOR * FACTOR = PRODUCT 2 * 2 * 2 = 8

THE NUMBER OF TIMES BASE IS MULTIPLIED BY ITSELF

2

2{1st time} * 2{2nd time} * 2{3rd time} =40

81)3333(34 means

81)3()3()3()3()3( 4 means

27)333(33 means

27)3()3()3()3( 3 means

2 SAY 2 TO THE 2nd POWER OR

TWO SQUARED MOST MATHEMATICIAN SAY TWO SQUARED

2 = 2 2 = 4

2 SAY 2 TO THE 3rd POWER OR TWO CUBED

MOST MATHEMATICIANS SAY TWO CUBED

2 = 2 2 2 =8

THE BASE IS ANY NUMBER BUT 0,THE ANSWER IS 1.

2 =1

4,638 =1 ANY NUMBER {except the number 0} =1

0 =UNDEFINED

THE ANSWER IS THE SAME NUMBER AS THE BASE NUMBER

2 =24,638 =4,638

ANY NUMBER =THE SAME BASE0 =0

THE EXPONENT 1 IS USUALY INVISIBLE

1. Write out the original problem.2. Show the substitution with parentheses.3. Work out the problem.

3;4: xxifSolveExample

3;4 xxifSolve

3)4( = 64

PRODUCT OF POWERS baba xxx

POWER TO A POWER baba xx

POWER OF PRODUCTaaa yxxy )(

ADD THE EXPONENTS

MULTIPLY THE EXPONENTS

This property is used when dividing two or more exponential expressions with the same base.

))()(())()()()((

3

5

xxxxxxxx

xx

2

1))(( xxx

7434

34

3

4

3 11111

xxxx

xxx

xx

Q1}Evaluate the variable expression when x = 1, y = 2, and w = -3 ?

22 )()( yx

22 )()( yx

22 )2()1(

541

Step 1

Step 2

Step 3

2)( yx

2)( yx

2)2()1(

9)3( 2

Step 1

Step 2

Step 3

ywx

ywx

2)1)(3(

Step 1

Step 2

Step 3

3)1)(3(

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