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Commutative Property of Multiplication

Commutative Property of Addition

Associative Property of Multiplication

Associative Property of Addition

Change of Order

Change of Order

Change of Parenthesis

Change of Parenthesis

Commutative Property of Multiplication

Change of Order

Commutative Property of Addition

Change of Order

zero exponents rule

power rule (powers to powers)

negative exponent rule for denominator

product rule

this says that anything raised to the zero power is 1 (ex: a…

this says that to raise a power to a power you need to multip…

negative exponents in the denominator get moved to the numera…

this says multiply two exponents with the same base, you keep…

zero exponents rule

this says that anything raised to the zero power is 1 (ex: a…

power rule (powers to powers)

this says that to raise a power to a power you need to multip…

Product Rule

Quotient Rule

Power Rule

Group of Factors

If the operation is MULTIPLICATION and the bases are the same…

If the operation is DIVISION and the bases are the same, keep…

When raising a Power, to a Power, keep the base and MULTIPLY…

Use the same rule as the Power rule on each factor in the group

Product Rule

If the operation is MULTIPLICATION and the bases are the same…

Quotient Rule

If the operation is DIVISION and the bases are the same, keep…

you add the exponents

you multiply the exponents

1

subtract the top exponent from the bot…

if you are multiplying powers with the same base..

raising a power to a power..

anything/itself

when dividing exponents with the same base

you add the exponents

if you are multiplying powers with the same base..

you multiply the exponents

raising a power to a power..

Product rule

Quotient rule

Zero exponent rule

Power rule

To multiply when two bases are the same, write the bases and…

To divide when two bases are the same, write the base and SUB…

Any base (except 0) raised to the zero power is one

To raise a power to another, write the base and MULTIPLY the…

Product rule

To multiply when two bases are the same, write the bases and…

Quotient rule

To divide when two bases are the same, write the base and SUB…

a **constant** is

7x-5... 7 is the ____... 5 is the ____

variables and the corresponding variables have the same expon…

a term that has no variable

a number that is multiplied by variable

coefficient, constant

variables and the corresponding variables have the same expon…

a **constant** is

a term that has no variable

Product of Powers

Power of a Power

Power of a Product

Negative Exponent

m n m+n... X * X = X

n... ( m) m*n... ( X ) = X

n n n... ( XY ) = X * Y

make a reciprocal and change the exponent sign... -n n... X = 1/X

Product of Powers

m n m+n... X * X = X

Power of a Power

n... ( m) m*n... ( X ) = X

P to the -8th power

C to the 22nd power

(H to the 18th power) 20th power

Y to the 36th power

P to the 4th power... ______________... P to the 12th power

C to the 12th power * C to the 10th power

H to the 180th power

(Y to the 4th power) 18th power

P to the -8th power

P to the 4th power... ______________... P to the 12th power

C to the 22nd power

C to the 12th power * C to the 10th power

1

2

3

4

When multiplying exponential expressions that have the same b…

When multiplying exponential expressions that have the same b…

When dividing exponential expressions that have the same base…

When dividing exponential expressions that have the same base…

1

When multiplying exponential expressions that have the same b…

2

When multiplying exponential expressions that have the same b…

the product rule

the quotient rule

raising a quotient to a power

raising a product to a power

When your bases are the same you keep the base and add the ex…

When your bases are the same you keep the base and subtract t…

the product rule

When your bases are the same you keep the base and add the ex…

the quotient rule

When your bases are the same you keep the base and subtract t…

Rule #1: If two exponents of the same…

Rule #2: If two exponents of the same…

Rule #3: If an exponent is being raise…

Rule #4: If an exponent is being raise…

add

subtract

multiply

1/x^5

Rule #1: If two exponents of the same…

add

Rule #2: If two exponents of the same…

subtract

the product rule

the quotient rule

raising a quotient to a power

raising a product to a power

When your bases are the same you keep the base and add the ex…

When your bases are the same you keep the base and subtract t…

the product rule

When your bases are the same you keep the base and add the ex…

the quotient rule

When your bases are the same you keep the base and subtract t…

Exponents

Base

Zero Exponent

Negative Exponent

Also known as the index or power, tells you how many times yo…

A term, variable, or number being raised to a power.

Any number raised to the zero power is equal to 1, except for…

Indicates reciprocation, with the exponent of the reciprocal…

Exponents

Also known as the index or power, tells you how many times yo…

Base

A term, variable, or number being raised to a power.

Multiplication of numbers in exponenti…

Division of numbers in exponential form

More division rules in exponential form

More Multiplication rules in exponenti…

Keep the base - add the exponents.

Keep the base - subtract the exponents.

Keep the base - subtract the exponents.... Simplify all terms.

Multiply the coefficient, keep the base, add the exponents

Multiplication of numbers in exponenti…

Keep the base - add the exponents.

Division of numbers in exponential form

Keep the base - subtract the exponents.

the product rule

the quotient rule

raising a quotient to a power

raising a product to a power

When your bases are the same you keep the base and add the ex…

When your bases are the same you keep the base and subtract t…

the product rule

When your bases are the same you keep the base and add the ex…

the quotient rule

When your bases are the same you keep the base and subtract t…

Product Rule

Quotient Rule

Power to a Power Rule

Negative Exponent Rule

When your bases are the same you keep the base add the expone…

When your bases are the same you keep the base subtract the e…

When you have an exponent raised to another exponent you keep…

You reciprocate

Product Rule

When your bases are the same you keep the base add the expone…

Quotient Rule

When your bases are the same you keep the base subtract the e…

the product rule

the quotient rule

raising a quotient to a power

raising a product to a power

When your bases are the same you keep the base and add the ex…

When your bases are the same you keep the base and subtract t…

the product rule

When your bases are the same you keep the base and add the ex…

the quotient rule

When your bases are the same you keep the base and subtract t…

Product of power rule

Quotient of power rule

Power of a Quotient rule

Power to a Power Rule

When your bases are the same you keep the base and add the ex…

When your bases are the same you keep the base and subtract t…

When you have a quotient raised to a power, you get a quotien…

When you have an exponent raised to another exponent you keep…

Product of power rule

When your bases are the same you keep the base and add the ex…

Quotient of power rule

When your bases are the same you keep the base and subtract t…

Multiplication of numbers in exponenti…

Division of numbers in exponential form

More division rules in exponential form

More Multiplication rules in exponenti…

Keep the base - add the exponents.

Keep the base - subtract the exponents.

Keep the base - subtract the exponents.... Simplify all terms.

Multiply the coefficient, keep the base, add the exponents

Multiplication of numbers in exponenti…

Keep the base - add the exponents.

Division of numbers in exponential form

Keep the base - subtract the exponents.

Multiplication of numbers in exponenti…

Division of numbers in exponential form

More division rules in exponential form

More Multiplication rules in exponenti…

Keep the base - add the exponents.

Keep the base - subtract the exponents.

Keep the base - subtract the exponents.... Simplify all terms.

Multiply the coefficient, keep the base, add the exponents

Multiplication of numbers in exponenti…

Keep the base - add the exponents.

Division of numbers in exponential form

Keep the base - subtract the exponents.