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1 of 17
a number written as
a 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 =2
4,638 =4,638
ANY NUMBER =THE SAME BASE
0 =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 PRODUCT
aaa
yxxy =)(
ADD THE EXPONENTS
MULTIPLY THE EXPONENTS
This property is used when dividing two or more exponential
expressions with the same base.
))()((
))()()()((
3
5
xxx
xxxxx
x
x
= 2
1
))((
x
xx
==
743
4
34
3
4
3
1111
1
xxx
x
xx
x
x
x
=×=÷==
−
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
y
wx
y
wx
2
)1)(3(−
Step 1
Step 2
Step 3
3)1)(3( −=−
17

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Exponentsandpower 111211055016-phpapp02

  • 1.
  • 2.
  • 3. a number written as a base number with an exponent BASE EXPONENT LIKE THIS: 2 SAY 2 TO THE 5th POWER
  • 4. THE REPEATED FRACTION IN A MULTIPLICATON PROBLEM BASE = POWER FACTOR * FACTOR * FACTOR = PRODUCT 2 * 2 * 2 = 8
  • 5. THE NUMBER OF TIMES BASE IS MULTIPLIED BY ITSELF 2 2{1st time} * 2{2nd time} * 2{3rd time} =40
  • 6.
  • 7. 81)3333(34 −=×××−− means 81)3()3()3()3()3( 4 =−×−×−×−− means 27)333(33 −=××−− means 27)3()3()3()3( 3 −=−×−×−− means
  • 8. 2 SAY 2 TO THE 2nd POWER OR TWO SQUARED MOST MATHEMATICIAN SAY TWO SQUARED 2 = 2 2 = 4
  • 9. 2 SAY 2 TO THE 3rd POWER OR TWO CUBED MOST MATHEMATICIANS SAY TWO CUBED 2 = 2 2 2 =8
  • 10. 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
  • 11. THE ANSWER IS THE SAME NUMBER AS THE BASE NUMBER 2 =2 4,638 =4,638 ANY NUMBER =THE SAME BASE 0 =0 THE EXPONENT 1 IS USUALY INVISIBLE
  • 12. 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
  • 13. PRODUCT OF POWERS baba xxx + =• POWER TO A POWER ( ) baba xx • = POWER OF PRODUCT aaa yxxy =)( ADD THE EXPONENTS MULTIPLY THE EXPONENTS
  • 14. This property is used when dividing two or more exponential expressions with the same base. ))()(( ))()()()(( 3 5 xxx xxxxx x x = 2 1 ))(( x xx == 743 4 34 3 4 3 1111 1 xxx x xx x x x =×=÷== −
  • 15. 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 y wx y wx 2 )1)(3(− Step 1 Step 2 Step 3 3)1)(3( −=−
  • 16.
  • 17. 17