Exponential rules

Exponential rules

Power is also called exponent, which is a small superscript number to the upper right of a larger number that explains how many times you multiply the larger number. (the larger number is called the base, the base of an exponent expression may number, positive, negative, fraction or radical).

Algebra is so hard working with when exponents have not being invented. Let say you are solving problems and you have to write variable z multiply three times, you will have to write zzz. 
That may not be seen complicated but think of six times(that is why you need to master exponent).
Exponents contain different rule, here are the rules:

RULE 1

xn
The base number of this expression is x and the exponent is n, it means x multiply by itself n times.
" x and n can`t be zero (0) at the same time. For instance 00, this means nothing in algebra and if x is 0, n can`t be negative.
Examples
1. 34 = 3 * 3 * 3 * 3 = 81.
2. 42 =  4 * 4 = 16.

RULE 2

xa * xb = xa+b
To multiply powers with the same base, pick the base and add the exponents together.
Examples:
1. 32 * 34 = 32+4 = 38> 2. 75 * 73 = 75+3 = 78
3. 24 * 25 * 27 * 210 = 24+5+7+10 = 226 (the bases are the same, so I choose one).
4. 52 * 35 * 53 * 34 =  52+3 * 35+4 = 55 * 39
5. 3x2y3x5y2 = 3x2+5 y3+2 =3x2y5 (collet the like terms and add the exponent).

RULE 3.

xa/xb = xa-b
To divide powers with the same base subtract the exponents and choose one from the base, but if the number base is divided, the divide.
Examples:
1. 25/24 = 25-4 = 21 =2
2. 2x2 / 4y4 /4y2 / 2x3 = 2x2-3 / 4y4-2 = 2x-1 / 4y2

RULE 4: 

Any number to the power of 0 equals 1, as long as the base is not 0,

a0=1, a ≠ 0
Examples:
1. 42/42 = 42-2 = 40 = 1.
2. 6x3y4z7/3x3y3z7 = 3x3-3y4-3z7-7 = 3x0y1z0 = 3y, because x⁰ and z0 are 1 each 3*1*y⁰*1 = 3y.

RULE 5.

x-a = 1/xa
The minus sign in front of the a is changed to 1 and it`s writing at the numerator while the base with it the exponent digit is written at the denominator.
Examples:
 1. 5-2 = 1/52 = 1/10.
2. 1/2-5 = 1/1/25 = 1 * 25/1 = 25.

RULE 6

(xn)m = xn*m
Expression xn is raised to the power of m so, the new power of x is determined by multiplying n together with m.
Examples:
1. (24)3 = 24*3 = 212 .
2. (5-2)-3 = 5-2*-3 = 56 .
Working with signed number
3. (3-2)5 = 3-2*5 = 3-10 = 1/310 .

RULE 7.

√is called radical
When you have a number or digit that is raised to the power, recall that I say the base is multiply in the number of the power (22 = 2*2 = 4). Now when ever you are given a number and it`s put under the radical (square root), you are told to find what number multiply itself two times to give the number under the radical.
example
√4 = 2 * 2 because 22 is 4
√9 = 3 * 3, 32 is 9
√36 =6 * 6, also 62 is 36.
"Radical also rival to as a twin brother to power 2, they cancel their-self in some advanced algebra"