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P2: Properties of ExponentsPowerPoint Presentation

P2: Properties of Exponents

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P2: Properties of Exponents

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Ex #7

- SIMPLIFY:

- If b is a real number and n is a natural number,

- bn is read “the nth power of b” or “ b to the nth power.” Thus, the nth power of b is defined as the product of n factors of b.
- Furthermore, b1 = b

Song:

http://www.youtube.com/watch?v=VQsQj1Q_CMQ

More serious tutorial video you can watch at home if you get stuck:

http://www.youtube.com/watch?v=Kr16rdBMX4o

b m · b n = b m+n

Ex #1

- YOU TRY:
- 33 • 32
- b. (4x3y4)(10x2y6)

When multiplying exponential expressions with the same base, add the exponents.

Ex #2

When dividing exponential expressions with the same nonzero base, subtract the exponent in the denominator from the exponent in the numerator.

Ex #2

b0 = 1

Any nonzero base

raised to the power of “0” equals 1

Ex #3

Cross the line to change the sign of the exponent.

Ex #4

(bm)n = bm•n

When an exponential expression is raised to a power, multiply the exponents.

Ex #5

(abn) = anbn

When a product is raised to the power, raise each factor to that power.

Ex #6

When a quotient is raised to a power, raise the numerator to that power and divide by the denominator to that power.

Both the numerator and the denominator are raised to that power.

PRODUCT

ZERO & NEGATIVE

- Multiplying same bases
- Power to a power
- Power of a product

QUOTIENT

- Any nonzero number raised to the “0” power = 1
- How do negative exponents become positive?

- Dividing same bases
- Power of a quotient