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# P2: Properties of Exponents - PowerPoint PPT Presentation

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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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)

Put it all together and what to you got???

• SIMPLIFY:

THE END!HW: pg. 28 #1 – 35 eoo, 37 – 63 odd

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

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.

The Quotient Rule

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

The Quotient Rule explainsZero as an Exponent

b0 = 1

Any nonzero base

raised to the power of “0” equals 1

Negative Exponents

Cross the line to change the sign of the exponent.

The Product Rule explainsPowers to Powers

(bm)n = bm•n

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

Products to Powers

(abn) = anbn

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

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