The exponent indicates the number of times the base is used as a factor. BASE EXPONENT POWER = 2x2x2x2x2=32

Zero Exponents Any number raised to the zero power equals one! Ex) Ex) Ex) Another important note: All numbers or variables have an exponent of ONE. So, x is the same as and 3 is the same as and so on. = 1

Placement of the Negative Placement of the negative is important! For example, when simplifying an expression you have to follow the order of operations means square 2 and then mult. by -1. But means multiply -2 by-2

Your Turn = -16= 16 = 1 = -1 (-1) = 1 = -1 = -3

When multiplying numbers or variables with like bases ADD the exponents. Think about it. Say you’re multiplying x 3 ·x 2. X3 means x·x·x and x 2 means x·x. So x·x·x·x·x = x 5. Add the exponents to get the correct power.

Example 3 You Try It!

NOTE: Multiply the coefficients and add the exponents on the like bases. Leave the bases the same. Example 4

Example 5

Example 6

Example 7

Power of a Power To Find the Power of a Power, Multiply the EXPONENTS. –For Instance: (a m ) n = a m*n Be sure to multiply the exponent outside the parentheses by all of the exponents inside the parentheses!

(x 3 ) 4 Example 1 =x 12

(x 2 ) 3 Example 2 x6x6

Example 3

52m652m6 Example 4 or 25m 6

Example 5

Answer or

We can divide two quantities with exponents if they have the same base. To divide two quantities with the same base, subtract the exponents and keep the base the same.

Example 1

Example 2 You Try It!

Example 3 You Try It! or 32

NOTE: Simplify the fraction part and subtract the exponents. Example 4

or

NOTE: Simplify the fraction part and subtract the exponents. Example 5

Let’s define a number with a negative exponent to be the reciprocal of that power with a positive exponent. So, to simplify an expression with a negative exponent, take the reciprocal, and make the exponent positive.reciprocal –For Instance:

In other words, move the factor with the negative exponent to the other side of the fraction bar and make the exponent positive. So, if a factor with a negative exponent is in the numerator, move it to the denominator and make the exponent positive, and vice versa.

Example 1

Example 2

or

Hint: the negative exponent only applies to the number or variable it is directly beside Example 3

Example 4

The exponent indicates the number of times the _____ is used as a _______. _________ __________ _________ = _______________

Zero Exponents Any number raised to the zero power equals one! Ex) Ex) Ex) Another important note: All numbers or variables have an exponent of ONE. So, x is the same as and 3 is the same as and so on. = __

Placement of the Negative Placement of the negative is important! For example, when simplifying an expression you have to follow the order of operations means square 2 and then mult. by -1. But means multiply -2 by -2

Your Turn (-1)

When multiplying numbers or variables with like bases _____ the exponents. Think about it. Say you’re multiplying x 3 ·x 2. X 3 means x·x·x and x 2 means x·x. So x·x·x·x·x = x 5. Add the exponents to get the correct power.

Example 3 You Try It! Remember to keep the base the same.

NOTE: Multiply the coefficients and add the exponents on the like bases. Leave the base the same. Example 4

Example 5 You Try It!

Example 6

Example 7

Power of a Power To Find the Power of a Power, ________ the EXPONENTS. –For Instance: (a m ) n = a m*n Be sure to multiply the exponent outside the parentheses by all of the exponents inside the parentheses!

(x 3 ) 4 Example 1

(x 2 ) 3 Example 2

Example 3

Example 4

Example 5

We can divide two quantities with exponents if they have the same base. To divide two quantities with the same base, ________________________ and ______________.

Example 1

Example 2 You Try It!

Example 3 You Try It!

NOTE: Simplify the fraction part and subtract the exponents. Example 4

NOTE: Simplify the fraction part and subtract the exponents. Example 5

Let’s define a number with a negative exponent to be the reciprocal of that power with a positive exponent. So, to simplify an expression with a negative exponent, take the reciprocal, and make the exponent positive.reciprocal –For Instance:

In other words, move the factor with the negative exponent to the other side of the fraction bar and make the exponent positive. So, if a factor with a negative exponent is in the numerator, move it to the denominator and make the exponent positive, and vice versa.

Example 1

Example 2

Hint: the negative exponent only applies to the number or variable it is directly beside Example 3

Example 4