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Math 1315-003

by: Alexis Williams

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Math 1315-003 MATH 1315 - 003

Alexis Williams
UTA

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COURSE
COLLEGE ALGEBRA FOR ECONOMICS & BUSINESS ANALYSIS
PROF.
Shelley D Hamilton
TYPE
Class Notes
PAGES
2
WORDS
KARMA
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This 2 page Class Notes was uploaded by Alexis Williams on Sunday September 11, 2016. The Class Notes belongs to MATH 1315 - 003 at University of Texas at Arlington taught by Shelley D Hamilton in Fall 2016. Since its upload, it has received 6 views. For similar materials see COLLEGE ALGEBRA FOR ECONOMICS & BUSINESS ANALYSIS in Math at University of Texas at Arlington.

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Date Created: 09/11/16
1.5 Exponents and Radicals Math 1315-003 Shelley Hamilton Division with Exponents:  5^7/5^4 = 5^7-4 = 5^3  (-8) ^10/ (-8) ^5 = (-8) ^10-5 = (-8) ^5  (3c) ^9/(3c) ^3 = (3c) ^9-3 = (3c) ^6  (7*19) ^3 = (7*19) (7*19) (7*19) = 7*7*7*19*19*19 = 7^3 * 19^3 When dividing exponents, you just subtract the exponents as you can see in the examples above. Product to a power:  (ab)^n = a^n * b^n  Ex. (5y) ^3 = 5^3 y^3 = 125y^3  (c^2 d^3) ^4 = (c^2) ^4 (d^3) ^4  (x/2) ^6 = x^6/2^6 = x^6/64  (a^4/b^3) ^3 = a^12/b^9  When multiplying when there is an exponent in and one outside of the (). You multiply them together. Also, that exponent outside of the parenthesis, you distribute it in with the coefficient. Or every variable in the parentheses. Quotient to a Power:  (a/b) ^n = a^n/b^n  Same here you distribute the exponent outside of the parentheses into each variable. Negative Exponent:  a^-n = 1/a^n  3^-2 = 1/3^2 = 1/9  5^-4 = 1/5^4 = 1/625  X^-1 = 1/x^1 = 1/x  -4^-2 = -1/4^2 = 1/16  When dealing with negative exponents, to make the exponent positive you simply just put a one over it and it will make the exponents positive as you can see in the examples above. Inversion Property:  (a/b) ^-n = (b/a) ^n  Ex. (5/8) ^-1 = 8/5  (1/2) ^-5 = (2/1) ^5 = 2^5/1^5 = 32/1  (2/5) ^-3 = (5/2) ^3 = 5^3/2^3 = 125/8  (3/x) ^-5 = (x/3) ^5 = x^5/3^5 = x^5/243  When dealing with inverse properties. You simply just change the problem to its inverse so the exponent can be positive. 1.5 Exponents and Radicals Math 1315-003 Shelley Hamilton ***These notes come from the lectures and the textbook : Applications in Mathematics

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