#### Study sets matching "algebra rules exponents"

#### Study sets matching "algebra rules exponents"

Product of powers

Power of a power

Power of a product

Quotient of powers

If multiplying two numbers with the same base, add the expone…

If raising a power to a power, multiply the exponents.

Find the power of each factor of the parenthesis and multiply.

If dividing two numbers with the same base, subtract the expo…

Product of powers

If multiplying two numbers with the same base, add the expone…

Power of a power

If raising a power to a power, multiply the exponents.

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…

Multiplying exponents with the same base

Dividing exponents with the same base

Raising an exponent to a power

Distributive Property of Exponents

If the numbers have the same base, you can add the powers.

If the numbers have the same base, you can subtract the powers.

If a base raised to a power is again raised to another power,…

A multiplication raised to a power can be written as multiple…

Multiplying exponents with the same base

If the numbers have the same base, you can add the powers.

Dividing exponents with the same base

If the numbers have the same base, you can subtract the powers.

Product Rule

Quotient Rule

Zero Exponent Rule

Power Rule

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

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

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

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

Product Rule

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

Quotient Rule

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

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…

Monomials

Degree of a Monomial

Rule for Multiplying Exponential Expre…

Rule for Simplifying a Power of an Exp…

A number, variable, or a product of a number and variables.

The sum of the exponents of the variables.

If m and n are integers, then x^m • x^n = x^m+n

If m and n are integers, then (x^m)^n = x^mn

Monomials

A number, variable, or a product of a number and variables.

Degree of a Monomial

The sum of the exponents of the variables.

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…

**like terms**have the same

a

**constant**is**coefficient**of a term

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

**like terms**have the same

variables and the corresponding variables have the same expon…

a

**constant**isa term that has no variable

Product of a power

Power of a power

Power of a product

Quotient of a power

Keep the base add the exponents 2^2 x 2^3 = 2^5

Multiply the exponents (2^2)^3 = 2^6

Apply the exponents to the base (9x)^2 = 9^2 x^2

Division with same base, subtract exponents y^6/y^2 = y^6-2 =…

Product of a power

Keep the base add the exponents 2^2 x 2^3 = 2^5

Power of a power

Multiply the exponents (2^2)^3 = 2^6

x^24•x^40= x^65

X^36/x^13 =x^23

(X^5)12 = x^60

4^0 = 1... 0^0 = undefined

When multiplying quantities with the same base, add the expon…

When dividing quantities with the same base, subtract exponda…

When a quantity raised to an exponent is rises to another exp…

And number to the zero power is one. Except 0^0

x^24•x^40= x^65

When multiplying quantities with the same base, add the expon…

X^36/x^13 =x^23

When dividing quantities with the same base, subtract exponda…

add the exponents

subtract the exponents

multiply the exponents

the exponents stay the same

when the bases are multiplied...

when the bases are divided...

when the bases are raised to a power...

when the bases are added or subtracted...

add the exponents

when the bases are multiplied...

subtract the exponents

when the bases are divided...

Multiplying powers with same bases.

Dividing powers with same bases.

Raising a power to an exponent.

Multiplying powers within same exponent

(X^m)(X^n) = X^(m+n)

(X^m) / (X^n) = X^(m-n)

(X^m)^n = X^(m x n)

(X^n) x (Y^n) = (X x Y)^n

Multiplying powers with same bases.

(X^m)(X^n) = X^(m+n)

Dividing powers with same bases.

(X^m) / (X^n) = X^(m-n)

when multiplying like bases...

when raising a power to a power...

when raising a product to a power or m…

when diving like bases...

add the exponents

multiply the exponents

everything gets the power

subtract the exponents

when multiplying like bases...

add the exponents

when raising a power to a power...

multiply the exponents

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..

multiplying powers

dividing powers

raising a power to a power

negative exponents

base stays the same, add the exponents... if there are number co…

base stays the same, subtract the exponents... if there are numb…

base stays the same, multiply the exponents... if there is more…

only the number or variable with the negative exponent gets m…

multiplying powers

base stays the same, add the exponents... if there are number co…

dividing powers

base stays the same, subtract the exponents... if there are numb…

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

exponents with addition and subtraction

exponents with multiplication and divi…

if there is a negative power...

If the exponent is 0...

powers must be the same

bases must be the same.

you must rewrite the monomial as a fraction. ex. N⁻²= 1/N²

the monomial equals 1.

exponents with addition and subtraction

powers must be the same

exponents with multiplication and divi…

bases must be the same.

Product of Power Property

Power of a Power Property

Power of a Product Property

Zero Exponent Rule

aⁿ×aⁿ=aⁿ⁺ⁿ... 5²×5³=5²⁺³=5⁵

(aⁿ)ⁿ=aⁿ×ⁿ... (5²)³=5²×³=5⁶

(ab)ⁿ=aⁿ×bⁿ... (5×4)²=5²×4²=25×16

a⁰=1... 5⁰=1... ⁻5⁰= ⁻1... (⁻5)⁰=1

Product of Power Property

aⁿ×aⁿ=aⁿ⁺ⁿ... 5²×5³=5²⁺³=5⁵

Power of a Power Property

(aⁿ)ⁿ=aⁿ×ⁿ... (5²)³=5²×³=5⁶

what are exponents?

using the product rule

the quotient rule

zero exponent rule

1²... 1= base... ₂= exponent

same bases being multiplied to different powers, add the expo…

when dividing with the same base, subtract your exponents

b⁰=1

what are exponents?

1²... 1= base... ₂= exponent

using the product rule

same bases being multiplied to different powers, add the expo…

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…

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.

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

Product of Powers

Power of a Power

Power of a Product

Quotient of Powers

Base stays the same; add the powers

Base stays the same; multiply the powers

Raise each factor to the power

Base stays the same; subtract powers

Product of Powers

Base stays the same; add the powers

Power of a Power

Base stays the same; multiply the powers

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…

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.