Power - a way of describing the exponent in exponential notation We - PowerPoint PPT Presentation

D AY 96 – E XPONENTIAL R ULES REVIEW

V OCABULARY Base - the value that is raised to a power when a number is written in exponential notation In the tone 5 3 , 5 is the base and 3 is the exponent. Exponent - the value that indicates the number of times another value is multiplied by itself in exponential rotator The exponent, also called the power, is written in superscript In the term 5 3 , 5 is the base and 3 is the exponent. Exponential notation - a condensed way of expressing repeated multiplication of a value by itself Exponential notation consists eta base and an exponent In the exponential term 5 3 , 5 is the base and 3 is the exponent This is a shorthand way of wring 5*5*5. Also called exponential form

Power - a way of describing the exponent in exponential notation We can say the base is raised to the power of the exponent. For example we read x 5 as "x raised to the 5 th power.“ power of a power - raising a value written in exponential notation to a power as in (x 2 ) 3 product of powers - multiplication of two or more values in exponential form that have the same base — the base stays the same and the exponents are added. quotient of powers - division of two or more values in exponential form that have the same base — the base stays the same and the exponent in the denominator is subtracted from the exponent in the numerator

Z ERO -E XPONENT R ULE : a0 =1. this says that anything raised to the zero power is 1.  0 3 1  3 4 0 ( 5 x y ) 1

P OWER R ULE (P OWERS TO P OWERS ): (a m ) n = a mn . This says that to raise a power to a power you need to multiply the exponents. There are several other rules that go along with the power rule, such as the product-to-powers rule and the quotient-to-power rule.  5 4 20 ( x ) x   4 2 3 3 12 6 12 6 ( 2 x y ) 2 x y 8 x y 4   2 4 x x      5 20   y y

N EGATIVE E XPONENT R ULE : 1   n a 1 1 n this says the a    2 5 negative exponents in the 2 numerator get moved to 5 25 the denominator and become positive exponents. 4   Negative exponents in the 2 4 x denominator get moved to 2 x the numerator and become positive exponents. Only  3 7 move the negative x y  exponents.  7 3 y x

P RODUCT R ULE : a m  a n = a m+n . this says that to multiply two exponents with the same base. You keep the base and add the powers.   5 6 x x x   4 9 13 y y y

Q UOTIENT R ULE : 5 x n a    m n 2 a x ,this says that to n a divide two exponents with the 3 x same base, you keep the base and subtract the powers. This is 4 similar to reducing fractions; y 1  when you subtract the powers put the answer in the 9 5 y y numerator or denominator depending on where the higher power was located. If the higher 3 2 power is in the denominator, put x y x  the difference in the denominator and vice versa, this 2 5 3 x y y will help avoid negative exponents.

E XAMPLE         4 3 1 b a           Rewrite as a product  Simplify   5     1 1 c of fractions     4 3 b a       Rewrite variables 1 1 1        with negative powers 5 c       4 3 1 following the rule for b a   negative exponents:   5 c a -n = 1 n a       5 Simplify division by a 1 1 c       fraction       4 3   b a 1 5 c Multiply fractions 4 3 b a 5 c ANSWER 4 3 b a

E XAMPLE 2 Simplify 5 5 x 3 3 x 5 5 x 5 xxxxx 5 xxxxx   3 3 3 3 x xxx xxx 2 5 xx 5 x 5    2 x 3 3 3

E XAMPLE 3 Use the one to one property to solve for the variable.    5 1. 3 2 x x 5   3 3 2 a a 2.

E XAMPLE 3 Use the one to one property to solve for the variable.    2 p 2 p 1 4 4 3.

A NSWER Use the one to one property to solve for the variable.    5 1. 3 2 x x 5    3 2 x x  3 x   3 3 2 a a 2.   2 a a  3 a 0  a 0

A NSWER Use the one to one property to solve for the variable.    2 p 2 p 1 4 4 3.    2 p 2 p 1   4 p 1 1   p 4