an-m = an/am
an+m = an ∙ am
a-n = 1/an
anm = anam = (an)m = (am)n
anbn = (ab)n
n√a = a(1/n)
n√(a b) = n√a ∙ n√b
n√(a/b) = ( n√a) / ( n√b)
n√(am) = (am)(1/n) = a(m/n) = (n√a)m
(a/b)n = an / bn
a0 = 1
a1 = a
Example 1:
24/22 = (2*2*2*2 ) / (2*2) = 24-2 = 22
Example 2:
2324 = 23+4 = 27
Example 3:
2434 = (2*3)4 = 64
Example 4:
[3/2]4 = 34 / 24
Example 5:
3-2 = 1 / 32
Example 6:
(32)4 = 3(2*4) = 38
Exponential Powers Grow Expressions Rapidly
Exponential powers increase the value of an expression at an incredibly large rate. In order to see this, consider the following example:
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
28 = 256
29 = 512
In each instance, the value is doubling, which makes sense since it is being multiplied by 2 another time for each increase in the value of the exponent.
Example 7:
A carpenter cuts a wooden box randomly. He finds that one of the pieces cut was square in shape and its side measure was 115 of a meter. Find the area of the square.
Area of a square = side x side = s2
Substitute in place of s, (s= 115)
Area of a square = 1225
The area of the square is 1225m2.
Example 8:
Find the value of m that makes the expression (5jm)3 = 125j9 valid.
125j9 can be written as (5j3 x 5j3 x 5j3), which is the same as (5j3 x 5j3 x 5j3) = (5j3)3.
So, the value of m in the expression (5jm)3 is 3.