1. Laws of Exponents
x2y4(xy3)2 X2 X3

2. X0 = 1 Zero Rule 990= 1 Examples: 20=1
Any non-zero number raised to the
zero power equals one
X0 = 1
Examples: 20=1
990= 1
That seems wrong!
Anything to the zero power is equal to 1 !?!?
…Well click on the information button for an explanation!

3. Any number raised to the power of one equals itself.
Rule of One
Any number raised to the power of one equals itself.
x1=x
Examples: 171 = 17
991 = 99
Well this one is easy!

4. Product Rule xa • xb = xa+b
When multiplying two powers with the same base, keep the base and add the exponents.
xa • xb = xa+b
Examples : 42 • 43 = 45
95 • 98 = 913
Now here’s a harder one! (x2y4) (x5y6) = x7y10

5. Quotient Rule xa ÷ xb = xa-b
When dividing two powers with the same base, keep the base and subtract the exponents.
xa ÷ xb = xa-b
Examples : 75 ÷ 73 = 72
28 ÷ 22 = 26
Remember that division can also be written vertically:
Now here’s a harder one!

6. But what happens if you add or subtract the exponents and you get a negative number ?
First of all, there is no crying in math! Second, we have a law for that too! It’s called the Negative Rule! Let me tell you all about it…

7. Negative Rule
Any non-zero number raised to a negative power equals its reciprocal raised to the opposite positive power.
WHAT!!
Click on this button to read more about it!

8. …Negative Rule
Remember that a reciprocal is the multiplicative inverse. In simple terms, flip the fraction! The reciprocal of is .
If we apply the negative rule (Any non-zero number raised to a negative power equals its reciprocal raised to the opposite positive power) then,
A non-zero
raised to a negative power =
The reciprocal raised to the opposite power
In this example, the negative in front of the four remains. Only the negative of the exponent is effected.

9. Let me jot this down. Oh yes, I got it now!
Power Rule
When raising a power to a power, keep the base and multiply the exponents.
(xa)b = xa•b
Let me jot this down. Oh yes, I got it now!
Examples: (24)3 = 212
(x3)5 = x15

10. Tricky, trickier, trickiest – But I think I got it!
Product to a Power Rule
A product raised to a power is equal to each base in the product raised to that exponent.
(x • y)2 = x2y2
Examples:
(7• 3)2 = 72 •32 = 49 • 9 =441
(x3y2)5 = x15y10
(2x2yz-3)-4 = 2-4x-8 y-4 z12 = =
Here’s one where the variables have exponents
Here’s one where the product is raised to a negative power!
Tricky, trickier, trickiest – But I think I got it!

11. Quotient to a Power Rule
A quotient raised to a power is equal to each base in the numerator and denominator raised to that exponent.
Examples:
…and this is the last law!

12. Why does anything to the zero power equal 1?
Take the product for 25 and divide it by 2.
32 ÷ 2 = 16 and 16 = 24
Now take that answer, 16, which is the standard form of 24, and divide it by 2.
16 ÷ 2 = 8 and 8= 23
Now take that answer, 8, which is the standard form of 23, and divide it by 2.
8 ÷ 2 = 4 and 4= 22
Now take that answer, 4, which is the standard form of 22, and divide it by 2.
4 ÷ 2 = 2 and 2 = 21
Now take that answer, 2, which is the standard form of 21, and divide it by 2.
2 ÷ 2 = 1 AND 1 = 20
Division is a good way of showing how this works:
22 = 2 x 2 = 4
21 = 2 = 2
23 = 2 x 2 x 2 = 8
24 = 2 x 2 x 2 x 2 = 16
25 = 2 x 2 x 2 x 2 x 2 = 32
20 = 1 = Really!
THIS WORKS FOR ALL NUMBERS – CLICK HERE TO SEE ONE MORE EXAMPLE!

13. Take the product for 55 and divide it by 5
3125 ÷ 5 = 625
and 625 = 54
Now take that answer, 625, which is the standard form of 54, and divide it by 5
625 ÷ 5 = 125
and 125 = 53
Now take that answer, 125, which is the standard form of 53, and divide it by 5
125 ÷ 5 = 25
and 25 = 52
Now take that answer, 25, which is the standard form of 52, and divide it by 5
25 ÷ 5 = 5
and 5 = 51
Now take that answer, 5, which is the standard form of 51, and divide it by 2.
5 ÷ 5 = 1
AND THEREFORE =50
52 = 5 X 5= 25
51 = 5 = 5
50 = 1
53 = 5 X 5 X 5= 125
54 = 5 X 5 X 5 X 5 = 625
55 = 5 X 5 X 5 X 5 X 5 = 3125
Click to go back to where I left off