The goal for this investigation was to understand exponents and learn how to use them. By completing this unit students shoul understand why and how the exponents work and the task analysis or algorithms to solve a problem.
Key Vocabulary:
Base - The face of a 3-Dimensional shape, chosen to be the bottom base.
Exponent - A symbol or number placed above and after another symbol or number to denote the power in which later is to be raised.
Task Analysis:
Multiplication Properties of Exponents:
1) Product of Powers property
To multiply powers having the same base, add the exponent.
In General: a^m*a^n=a^m+^n
Examples:
1. 3^2*3^7= 3^2+^7=3^9
2. 3*3^5=3^1+^5=3^6
3. (-2)^2+(-2)^4=(-2)^6
4. x^2*x^3*x^4=x^9
2) Power of a Power Property
To find a power of a power,multiply the exponent.
In General: (a^m)^n=a^m*^n
Examples:
1. (5^2)^4=5^2*4=3^8
2. (y^3)^4=y^12
3. [(y^3)^3]^2=-3^6
2. 3*3^5=3^1+^5=3^6
3. (-2)^2+(-2)^4=(-2)^6
4. x^2*x^3*x^4=x^9
2) Power of a Power Property
To find a power of a power,multiply the exponent.
In General: (a^m)^n=a^m*^n
Examples:
1. (5^2)^4=5^2*4=3^8
2. (y^3)^4=y^12
3. [(y^3)^3]^2=-3^6
Division Properties of Exponents
1) Quotient of Powers Property
To divide powers having the same base, subtract exponents.
In General: a^m/a^n=a^m-n
Ex:
1. 6^5/6^4=6^1=6
2. 9^4*9^2/9^7=9^6/9^7=9^-1
3. (-5^2)/(-5^2)=(-5^0)=1
4. y^3/y^5=y^-2
2) Power of a Product or Quotient Property:
To find a power of a product or quotient, distribute the exponent over the factors.
In General: (a*b)^m=a^m*b^m
(a/b)^m=a^m/b^m
Ex:
1. (6*5)^2=6^2*5^2
2. (4yz)^3=4^3*y^3*z^3
3. (2/3)^2=2^2/3^2
4. (7/4)^-3=7^-3/4^-3=4^3/7^3
For more help visit:
http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_ExponentsRules.xml
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