# Exponents and Pythagorean Theorem ```Exponents
Exponents are a shorthand way to show how many times a number, called the base
number, is multiplied times itself. A number with an exponent is said to be &quot;raised
to the power&quot; of that exponent.
Base Number --
5
3 -- Exponent
The exponent indicates how many times in a row you multiply the base number.
Examples:
10 0 = 1
50 = 1
20 = 1
101 =10
51 = 5
21 = 2
102 = 10 &times;10 = 100
5 2 = 5 &times; 5 = 25
22 = 2 &times; 2 = 4
103 = 10 &times;10 &times;10 = 1,000
5 3 = 5 &times; 5 &times; 5 =125
23 = 2 &times; 2 &times; 2 = 8
Laws of Exponents
Law
Example
x1 = x
x0 = 1
x-1 = 1/x
xmxn = xm+n
xm/xn = xm-n
(xm)n = xmn
(xy)n = xnyn
(x/y)n = xn/yn
x-n = 1/xn
61 = 6
70 = 1
4-1 = 1/4
x2x3 = x2+3 = x5
x4/x2 = x4-2 = x2
(x2)3 = x2&times;3 = x6
(xy)3 = x3y3
(x/y)2 = x2 / y2
x-3 = 1/x3
Pythagorean Theorem
The theorem that relates the three sides of a right triangle:
a2 + b2 = c 2
a and b are the lengths of the two sides of the triangle that form the right angle.
c is the third side of the triangle which is known as the hypotenuse.
c
The length of any side of right triangle can be
found if you know the lengths of the other
two sides, and you use the Pythagorean
Theorem:
a
a2 + b2 = c 2
Remember, this only works for right triangles.
b
Example:
If side a equals 4 and side b equals 3, what is the
length of side c?
a=4
c
4
3
b=3
Using the Pythagorean Theorem:
a2 + b2 = c 2
↓
(4) 2 + (3) 2 = c 2
↓
16 + 9 = c 2 c 2 = 25
↓
c =5
c=?
```