Law of Exponent &Solving Exponential

FunctionBy: Ms. P

Algebra II, 9th grade

Introduction to Exponent

Definition: Exponent of a number says how many times to use the number in a multiplication

For example in 5⁴, the 4 means that we use 5 four times. So, 5⁴ = 5 x 5 x 5 x 5 x 5

Read as “five to the power of 4”

Exponents are also called Power or Indices

Intro to Exponent Cont.

Exponents make mathematical writing easier when use many multiplication.

So in general An tells you to multiply A by itself n times. In another word, there are n of those A

An = A x A x … x A

n

2 is the exponent value or index or power

8 is the base value

Your turn to practice;Expand and compare the difference between these two exponential terms.a) 27 and 72 b) 35 and 53 c)43 and 34

Negative Exponent

A negative exponent means it tells us to divide ONE by value of A after multiplying it n times

5-1 = 1 ÷ 5 = 0.28-5 = 1 ÷ ( 8 x 8 x 8 x 8 x 8 ) = 1 ÷ 32,768 = 0.0000305

Can you think of another way to solve 8-5 ?That’s right, we can rewrite the denominator in exponential form, so 8-5 = 1 / 85 = 1 / 32,768 = 0.0000305

In general : “take the reciprocal exponent”

What if the Exponent is 1, or 0?

A1 If the exponent is 1, then you just have the number itself (example 91 = 9) A0 If the exponent is 0, then you get 1 (example 90 = 1)

Your turn; Please solvea) 4-2 b)10-3 c) (-2)-3

Law of Exponents or Rules of Exponents

We can add exponents (n) if we have the same multiply two values with the same base (A). Why?Remember that 5⁴ = 5 x 5 x 5 x 5 x 5So if we want compute 5⁴ * 53 =( 5 x 5 x 5 x 5) * (5 x 5 x 5 ) =( 5 x 5 x 5 x 5 5 x 5 x 5 ) = 57

So, 5⁴ * 53 = 5⁴+3 = 57

Video Explanationhttps://www.youtube.com/watch?v=VQsQj1Q_CMQ

REMEMBER!

Law of Exponents or Rules of Exponents Cont.

We can add exponents (n) if we have the same multiply two values with the same base (A). Why?Remember that 5⁴ = 5 x 5 x 5 x 5 x 5So if we want compute 5⁴ * 53 =( 5 x 5 x 5 x 5) * (5 x 5 x 5 ) =( 5 x 5 x 5 x 5 5 x 5 x 5 ) = 57

So, 5⁴ * 53 = 5⁴+3 = 57

Video Explanationhttps://www.youtube.com/watch?v=VQsQj1Q_CMQ

Solving Exponential Equation

As you complete solve these equations, please answer the following questions;1)Identify the base and the power2)Please simplify and solve, if possible. 3)What law of exponent did you use? Please state the reason if a

problem cannot be solvedWork must be shown.

i) (x½)6 ii)(2½)4 * (2¼)8

iii) (3½)6 * (4½)8 iiv)(2¼)16 * (4½)8

(3)2 * 42

Rewrite exponential expression

Think of how you may solve for this problem;

Solve 5x = 53 , Find x

That’s right! Both have the same base of “5” thus the only way the two expression can be equal to each other for their power or exponent to be the same,

Therefore, x = 3

What if the bases are not the same? Can we still solve the equation?

Think of this problem 5x=253

We know the bases are not the same, but can we rewrite 25 to have a base of 5? 25 can be written as 52

Therefore, we can rewrite the equation so they have a common base as5x=253 5x=(52)3

5x=56 Simplifyx = 6 Solve for x

Rewrite exponential expression Cont.

Now examine this problem. What if the exponent is negative? And the base is a fraction?

(1/2)x = 4 , solve for x

(1/2)x = 2 -1x quotient law of exponent4 = 22 rewrite 4 to have a common base of 22-1x =22 substituting to original equation2-x = 22 Simplify-x = 2 Solve for x

Therefore, x = -2

Solving Exponential Expression

Please write down the reason for each step to solve the exponential equations;(As I just did in the previous example)

1)9x=81 2) (1/4)x = 32

3) 4 2x+1 = 65 4) (1/9)x – 3 = 24

Next Lesson:

Tomorrow we will go over 1) Standard form of Exponential function 2) Graphing of exponential

function