Your SlideShare is downloading. ×
Exponents
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

Exponents

4,661
views

Published on

Published in: Education, Technology, Business

1 Comment
6 Likes
Statistics
Notes
No Downloads
Views
Total Views
4,661
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
180
Comments
1
Likes
6
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 1. Exponents
  • 2. Review:
    • What do exponents tell us?
    • What does 5 3 mean?
    • 5 3 =5  5  5
  • 3. What is the “base”? What is the “exponent”?
    • 8 5
    Base Exponent
  • 4.
    • Write 6 3 in standard form.
    • 6 3 = 6  6  6 = 216
  • 5. Write 6 4 in standard form.
    • 6 4 = 6  6  6  6
    • = 1,296
  • 6. What happens if we multiply
    • 6 3  6 4 ?
    • 6 3  6 4 =
    • (6  6  6)  (6  6  6  6)
    6 3 6 4
  • 7.
    • So…
    • 6 3  6 4 = 6 7 because we used 6 as a factor seven times!
    • Notice anything?
  • 8. Let’s try another example:
    • What is 5 2  5 4 ?
    • 5 2  5 4 = (5  5)  (5  5  5  5)
    • or 5 2  5 4 = 5 6
  • 9. For MULTIPLICATION:
    • x s  x t = x s + t
    • (For any number x and for integers s and t .)
  • 10.
    • In other words, when multiplying two numbers in exponential form with the same base , add the exponents.
  • 11.
    • Ex : 9 4  9 8 = ?
    • 9 12
  • 12. What happens if we divide? 7 5 7 3
    • 7 5 = 7  7  7  7  7
    • 7 3 7  7  7
    Cancel out any numbers that are in the numerator AND denominator!
  • 13.
    • After we cancel, we are left with 7 2 .
    • So, 7 5 = 7 2
    • 7 3
  • 14. For DIVISION:
    • x s =
    • x t
    • (For any nonzero number x and for integers s and t .)
    x s - t
  • 15.
    • In other words, when dividing two numbers in exponential form with the same base , subtract the exponents.
  • 16.
    • Ex: 6 8 ÷ 6 5 = ?
    • 6 3
  • 17. What about (5 2 ) 3 ?
    • (5 2 ) 3
    • (5 2 )  (5 2 )  (5 2 )
    • (5  5)  (5  5)  (5  5)
    • 5 6
  • 18. Raising a power to a power:
    • (x s ) t = x s  t
    • (For any number x and for integers s and t .)
  • 19.
    • In other words, when raising a number with an exponent to a power , multiply the exponents.
  • 20.
    • Ex :
    • (5 3 ) 7 = ?
    • 5 21
  • 21. One important thing to remember…
    • x 0 = 1
    • ( Any number to the zero power is equal to 1 !)
  • 22. Why???
    • For example…
    • 3 2 ÷ 3 2 = 3 2 - 2 = 3 0
    • 3 2 = 3  3 = 9 = 1
    • 3 2 3  3 9
  • 23.
    • So, 3 0 = 1
    • This works for any base number!
  • 24. Can we have negative exponents?
    • Yes! Negative exponents represent the reciprocal.
    • The reciprocal of x is The reciprocal of 10 is
    • They do NOT make the answer negative.
  • 25.
    • 5 -2 = =
    • 2 -4 =

×