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Division with Exponents & Negative and Zero Exponents
Essential Questions How do I use the division properties of exponents to evaluate powers and simplify expressions? How do I evaluate powers that have negative and zero exponents?
Activator Simplify 1. (3w 2 ) 2 2. (4vw 3 ) 2 3. (2xy 3 ) 4 (4x 2 y 5 ) Solutions: 1. 9w 4 2. 16v 2 w 6 3. 64x 6 y 17
Quotient of Powers Property To divide powers having the same base, subtract exponents. Example:
Power of a Quotient Property To find the power of a quotient, find the power of the numerator and the power of the denominator and then divide. Example:
Example 1 Simplify completely. 1. 2. = 6 1 = 6 = 4 2 = 16
Example 2 Simplify completely. 1.2.
Zero Exponents A nonzero number to the zero power is 1! a 0 = 1, a≠0 Example: 5 0 = 1
Hmmm…why is that true? Look at the following example: When we subtract exponents we get 4 0 ! So 4 0 = 1
Negative Exponents Negative exponents must be moved to the denominator! This makes them positive!! Example:
Example 3 Simplify 1. (-2) 0 = 1 2.
Example 4 Simplify
Try This! Simplify
Zero Exponent? Product or quotient of powers with the same base? Simplify Negative Exponents.
Vocabulary Chapter 7. For every nonzero number a, a⁰ =
The Laws of Exponents.
1)Be able to apply the quotient of powers property. 2)Be able to apply the power of a quotient property. 3)Be able to apply the multiplication properties.
Laws of Exponents: Dividing Monomials Division Rules for Exponents.
Exponents and Scientific Notation
EXAMPLE 2 Evaluate exponential expressions a. 6 – Product of a power property = 6 0 Add exponents. = 1 Definition of zero exponent = 6 –
Warm Up Simplify (10²)³
Exponents Power base exponent means 3 factors of 5 or 5 x 5 x 5.
Properties of Exponents
Exponents and Polynomials
6.1 Properties of Exponents
PROPERTIES OF EXPONENTS. PRODUCT OF POWERS PROPERTY.
Chapter 6 Polynomial Functions and Inequalities. 6.1 Properties of Exponents Negative Exponents a -n = –Move the base with the negative exponent to the.
WELCOME BACK Y’ALL Chapter 6: Polynomials and Polynomial Functions.
DISTRIBUTIVE PROPERTY AND POWER PROPERTIES You Control the Power!
Exponent Rules Essential Question: How can I simplify and evaluate algebraic equations involving integer exponents?
Dividing Monomials Chapter 8-2 S. Calahan To divide two powers that have the same base, subtract the exponents. b 15 ÷ b 7 = b 15-7 = b 8 Quotient.
Describe the pattern in the following example. Division Rule - When dividing two powers with the same base, subtract the exponents.
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