# P2: Properties of Exponents - PowerPoint PPT Presentation

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P2: Properties of Exponents. WARM UP – Copy the table below into your notes. Expand each problem and then simplify. PRACTICE – identify which rule applies and simplify (don’t need to expand). Practicing with Negative Exponents. (. Ex #7. Put it all together and what to you got???.

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P2: Properties of Exponents

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• (

Ex #7

• SIMPLIFY:

### A Natural Number Exponent

• 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

### OH YEAH!!! CHEESY VIDEO TIME:

Song:

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

b m · b n = b m+n

Ex #1

### The Product Rule

• YOU TRY:

• 33 • 32

• b. (4x3y4)(10x2y6)

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

Ex #2

### The Quotient Rule

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

Ex #2

### The Quotient Rule explainsZero as an Exponent

b0 = 1

Any nonzero base

raised to the power of “0” equals 1

Ex #3

### Negative Exponents

Cross the line to change the sign of the exponent.

Ex #4

### The Product Rule explainsPowers to Powers

(bm)n = bm•n

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

Ex #5

### Products to Powers

(abn) = anbn

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

Ex #6

### Quotients to Powers

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.

### PROPERTIES OF EXPONENTS(Graphical Organizer)

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