The example exponent above shows 2 to the power of 3. The long way to do the math for this problem is to multiply 2 x 2 x 2 = 8.
Mathematical Rules for Exponents
There are several rules that are applied to calculating exponents, as follows:
x 1 = x
For example 21 = 2
x 0 = 1
For example 20 = 1
ya × yb = y(a + b)
For example: 22 × 23 is the same as 2(2+3) = 25 = 32
ya/ yb = y(a - b)
For example: 24/ 22 is the same as 2(4-2) = 22 = 4
(ya)b = y(a * b)
For example: (22)2 is the same as 2(2 * 2) = 24 = 16
(x * y)a = xa * ya
For example: (2 * 3)2 is the same as 22 * 32 = 4 * 9 = 36
(x/y)a = xa / ya
For example: (2 / 4)2 is the same as 22 / 42 = 4 / 16 = 1/4
**note we are reducing 4/16 to 1/4 because 4 goes into 4 one time and 4 goes into 16 four times
y-a = 1 / ya
For example: 2-2 is the same as 1 / 22 = 1 / 4
(x / y)-a = ya / xa
For example: (2 / 4)-2 is the same as 42 / 22 = 16/ 4 = 4