1. What is an exponent?
The base A is raised to the power of (n) is equal to the multiplication of A, n times:
A n = A × A × ... × A
Examples
31 = 3
32 = 3 × 3 = 9
33 = 3 × 3 × 3 = 27
34 = 3 × 3 × 3 × 3 = 81

2. Bellwork Grab a new bellwork sheet
Simplify the following into exponential notation:
28 x 28
52 x 527
3x…x3=
12 times

3. Multiplication Rule Multiplication rule (product Rule)
a n · a m = a n+m
23 · 24 = 23+4 = 128
If bases are the same, keep the base and add the exponents together
Same Base

4. Whole number exponential notation
Write the following in exponential notation with a base number of 2: 8 16
128
256

5. Bellwork
The area of Mrs. Stoecker’s garden is 146 ft squared. How long is one side of her garden? Is it a perfect square?
Simplify if possible:
X2y5(y3)(X3y)
312 x 57 x 3 x 510

6. Division
to divide two exponents with the same base, you keep the base and subtract the powers.
67 / 63

7. Exponent raised to a power
When you have an exponent raised to a exponent, you keep the base then multiply the exponents (or powers).
( xm ) n = x m n
(x2)4 
= (x2)(x2)(x2)(x2) or (xx)(xx)(xx)(xx) 
= x8

8. continued

9. Bellwork
(-6) x … x (-6) = − Is this in correct notation? Why or why not
75 × 7x = What is x?
Simplify if possible, if cant tell why:
𝑎 10 𝑏 10
𝑥 7 5

10. What if the problem were upside down?
Negative Exponent
What if the problem were  upside down?  
A negative exponent means the base is on the wrong side of the fraction line, so you need to flip the base to the other side.

11. Continued
A negative exponent means the base is on the wrong side of the fraction line, so you need to flip the base to the other side.
Ex: 4-2
= 𝟏 42 or 𝟏 𝟏𝟔

12. ) ( a Negative Exponents 1 -n a
______ = n a
A nonzero base raised to a negative exponent is the reciprocal of the base raised to the positive exponent.

13. Zero Exponent A Zero exponent is investigated in much the same way.
  ,   as lo as long as   
 A Zero exponent is investigated in much the same way.    
If we subtract the exponents, we get:
If we cancel, we get: