Exponent Rules The exponent indicates the number of
Exponent Rules
The exponent indicates the number of times the base is used as a factor. EXPONENT BASE ER W O P = 2 x 2 x 2 =32
Zero Exponents Any number raised to the zero power equals one! Ex) = 1 = 1 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 = -16 (-1)4 = 1 = -3 = 16 -14 = -1
Product Rule for Exponents • When multiplying numbers or variables with like bases ADD 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 5. Add the exponents to get the correct power.
Example 1.
Example 2. You try it !!!
Example 3 You Try It!
Example 4 NOTE: Multiply the coefficients and add the exponents on the like bases. Leave the bases the same.
Example 5
Example 6
Example 7
Power of a Power • To Find the Power of a Power, Multiply the EXPONENTS. – For Instance: m n m*n (a ) = a Be sure to multiply the exponent outside the parentheses by all of the exponents inside the parentheses!
Example 1 3 4 (x ) 12 =x
Example 2 2 3 (x ) 6 x
Example 3
Example 4 2 6 5 m 6 25 m or
Example 5
Answer or
Quotient Rule for Exponents • 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
Example 4 • NOTE: Simplify the fraction part and subtract the exponents.
ANSWER or
Example 5 • NOTE: Simplify the fraction part and subtract the exponents.
Negative Powers • 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. – 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
ANSWER
Example 2
ANSWER or
Example 3 Hint: the negative exponent only applies to the number or variable it is directly beside
ANSWER
Example 4
Exponent Rules
The exponent indicates the number of times the _____ is used as a _______ _ _ __ _ _ = ________
Zero Exponents Any number raised to the zero power equals one! 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)4 -14
Product Rule for Exponents • 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 5. Add the exponents to get the correct power.
Example 1.
Example 2. You try it !!!
Example 3 You Try It! Remember to keep the base the same.
Example 4 • NOTE: Multiply the coefficients and add the exponents on the like bases. Leave the base the same.
Example 5 You Try It!
Example 6
Example 7
Power of a Power • To Find the Power of a Power, ____ the EXPONENTS. – For Instance: m n m*n (a ) = a Be sure to multiply the exponent outside the parentheses by all of the exponents inside the parentheses!
Example 1 3 4 (x )
Example 2 2 3 (x )
Example 3
Example 4
Example 5
Quotient Rule for Exponents • 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!
Example 4 • NOTE: Simplify the fraction part and subtract the exponents.
Example 5 • NOTE: Simplify the fraction part and subtract the exponents.
Negative Powers • 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. – 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
Example 3 Hint: the negative exponent only applies to the number or variable it is directly beside
Example 4
- Slides: 67