# Recently Added Math Formulas

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# Powers

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.

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