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Published byFrancis Rice
Modified over 5 years ago
OBJECTIVE: The students will simplify expressions by using the laws of exponents.
3x3 2x2x2x2x2x2 10x10x10 5x5x5 1x1x1x1x1x1x1x1 Write inexponential form 3x3 2x2x2x2x2x2 10x10x10 5x5x5 1x1x1x1x1x1x1x1
HISTORY of the word EXPONENT.The term EXPONENT was introduced by Michael Stifel ( ) in 1544 in Arithmetica integra.
An exponent is simply shorthand for multiplying that number of identical factors.
So 4³ is the same as (4)(4)(4), three identical factors of 4So 4³ is the same as (4)(4)(4), three identical factors of 4. And x³ is just three factors of x, (x)(x)(x).
Exponent is the power in an expression.13 7 Exponent BASE
Exponents exponent power base
Using the Calculator 5 4 Press 5 Press ^ Press 4 Then =
7 Laws of Exponents #1 PRODUCT LAWTo Multiply LIKE Bases… …Copy the Base, Add Exponents
Product Law or Product Rule
7 Laws of Exponents #2 QUOTIENT LAWTo Divide LIKE Bases… …Subtract Exponents a4
Quotient Law or Quotient Rule:
7 Laws of Exponents #3 EXPONENT of EXPONENT LAWTo Raise a Power to a Power… …Multiply Exponents a12
Exponent of Exponent Law or Exponential Rule:
7 Laws of Exponents #4 Raising a product to a powerTo Raise a QUANTITY to a Power, raise EACH Factor to that Power. (-3ab)2= 9a2b2
7 Laws of Exponents #5 Raising a quotient or a fraction to a powerTo Raise a FRACTION to a Power, raise BOTH Numerator & Denominator to that power. a4 b4
7 Laws of Exponents #6 NEGATIVE EXPONENT LAWNegative Exponents …Reciprocal with a Positive Exponent 1 ___ a3
#6: Negative Law of Exponents: If the base is powered by thenegative exponent, then the base becomes reciprocal with the positive exponent.
Any nonzero number raised to the ZERO Power = ONE7 Laws of Exponents #7 Any nonzero number raised to the ZERO Power = ONE 1 1 1
The Laws of Exponents: #7: Zero Law of Exponents: Any base powered by zero exponent equals one
Exponents exponent power base.
Zero Exponent? Product or quotient of powers with the same base? Simplify Negative Exponents.
The Laws of Exponents Animated floating petals (Difficult)
Laws of Exponents. Exponential Notation Base Exponent Base raised to an exponent.
Warm up Use the laws of exponents to simplify the following. Answer should be left in exponential form.
The Laws of Exponents.
Exponents and Scientific Notation
WHEN MULTIPLYING LIKE BASES, YOU ADD THE EXPONENTS FOR EXAMPLE: NOW YOU TRY:
Copyright©amberpasillas2010. Simplify two different ways. == = =
Dividing Monomials Honors Math – Grade 8. Quotient of Powers Look for a pattern in the exponents. 3 factors 5 factors KEY CONCEPT Quotient of Powers To.
Exponents Power base exponent means 3 factors of 5 or 5 x 5 x 5.
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.
Properties of Exponents
8-2 Dividing Monomials Objectives Students will be able to: 1)Simplify expressions involving the quotient of monomials 2)Simplify expressions containing.
Slide 1- 1 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Exponents base exponent means 3 factors of 5 or 5 x 5 x 5.
Chapter 7: Exponential Functions
Exponent Rules. Parts When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power.
Bell Ringer Solve. 1. 7x – 1 = 2x + 19
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