Powers and Laws of Powers and Laws of ExponentsExponents

SWBAT write the standard form for numbers that are SWBAT write the standard form for numbers that are given in exponential form; write the exponential form given in exponential form; write the exponential form

for numbers that are given in standard form; apply the for numbers that are given in standard form; apply the multiplication and division laws of exponents; identify multiplication and division laws of exponents; identify

the value of a number to the zero power; simplify the value of a number to the zero power; simplify expressions with exponents.expressions with exponents.

DefinitionsDefinitions

Exponent – tells you how many times a Exponent – tells you how many times a number is used as a factor (how many number is used as a factor (how many times you multiply it)times you multiply it)

Base – The factor (number) being Base – The factor (number) being multipliedmultiplied

3 ways to write exponents3 ways to write exponents

Exponential Exponential FormForm

Factored FormFactored Form Standard FormStandard Form

101033 10 x 10 x 1010 x 10 x 10 1,000 1,000

5599

6 x 6 x 6 x 6 x 6 6 x 6 x 6 x 6 x 6

100,000 100,000

5x5x5x5x5x5x5x5x5 1,953,125

65 7,776

105 10x10x10x10x10

Write each in simplest exponential Write each in simplest exponential formform

6 · 6 · 6 · 7 · 76 · 6 · 6 · 7 · 7 -1(-1)(-2)(-3)(-3)-1(-1)(-2)(-3)(-3) 2 · 2 · 2 · 2 · 2 · 2 · 22 · 2 · 2 · 2 · 2 · 2 · 2 10 · 10 · 10 · 10 · 10 · 10 · 10 · 1010 · 10 · 10 · 10 · 10 · 10 · 10 · 10

Multiplying ExponentsMultiplying Exponents

When they have the same base, keep the When they have the same base, keep the base number and add the exponentsbase number and add the exponents 2 · 22 · 222 · 2 · 244

55 · 5· 533

141466 · 14 · 1488

Dividing ExponentsDividing Exponents

When dividing exponents with the same When dividing exponents with the same base, keep the base and subtract the base, keep the base and subtract the exponents.exponents. 101099 ÷ 10 ÷ 1055

131388 ÷ 13 ÷ 1322

__5566__ 5522