1. Law of Exponent &
Solving Exponential Function
By: Ms. P
Algebra II, 9th grade

2. 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

3. 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

4. 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 = 0.2
8-5 = 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 solve
a) 4-2 b)10-3
c) (-2)-3

5. 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 5
So 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 Explanation
https://www.youtube.com/watch?v=VQsQj1Q_
CMQ
REMEMBER!

6. 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 5
So 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 Explanation
https://www.youtube.com/watch?v=VQsQj1Q_CMQ

7. Solving Exponential Equation
As you complete solve these equations, please answer the following questions;
1) Identify the base and the power
2) Please simplify and solve, if possible.
3) What law of exponent did you use? Please state the reason if a problem cannot be
solved
Work must be shown.
i) (x½)6 ii)(2½)4 * (2¼)8
iii) (3½)6 * (4½)8 iiv)(2¼)16 * (4½)8
(3)2 * 42

8. 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 as
5x=253 5x=(52)3
5x=56 Simplify
x = 6 Solve for x

9. 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 exponent
4 = 22 rewrite 4 to have a common base of 2
2-1x =22 substituting to original equation
2-x = 22 Simplify
-x = 2 Solve for x
Therefore, x = -2

10. 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

11. Next Lesson:
Tomorrow we will go over
1) Standard form of Exponential function 2) Graphing of exponential function