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# Exponents

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### 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 =