## Exponent Laws Math

Algebra is one of the most basic element of mathematics in which, we switch from basic arithmetic to variables. Here instead of using numbers we use different variables to represent different parameters. Algebra has various subdivisions like

z^m

where,

'z' is the base

'm' is the superscript

The various exponents law and examples for exponents used in math are given in the following sections.

The following

1. The law for the product exponents with same base,

a^m * a^n = a^m+n, provided a`!=` b

2. The law for exponents with zero superscript,

a^0 = 1, provided a`!=` 0

3. The law for exponents in fraction form,

`a^m/a^n` = a^m * a^-n , provided a `!=` 0

4. The law for exponents with whole superscript,

(ab)m = a^m * b^m , provided a`!=` b

5.The law for exponents with negative superscript,

a-m = `1/a^m`provided a`!=` 0

I have recently faced lot of problem while learning

6. The law for exponents with common superscript when the terms are in product,

(a^m b^m c^m) = (a*b*c)^m ,

`(a^m/b^m)` = (`a/b` )^m , provided a`!=` b

7. The law for exponents with radicals,

`root(n)(x^m)` = x`m/n`

`8. The law for exponents to exponents,`

(a^m)^n= a^mn

Simplify the math expression using laws of exponents , 22 * 23 * 22

Solution:

Since the base of the expressions are same, we can use the first law from the list shown above,

a^m * a^n = a^m+n, provided a`!=` b

Therefore,

22 * 23 * 22 = (2)2+3+2

= 27

= 128

Simplify the math expression using laws of exponents, `2^3 / 2^2`

Solution:

Using the exponents law three from the above listed laws,

`a^m/a^n` = a^m * a^-n , provided a `!=` 0

`2^3/2^2` = 23 *2-2

Using property 1 again,

= 23-2

= 2

Simplify the math expression using laws of exponents, (53 / 53) * 50

Solution:

Since the base of the expressions are same, we can use the sixth law from the list laws shown above,

`5^3/5^3` *50 = 1 * 50

Using the property 2,

= 1 * 1

= 1

Simplify the math expression using laws of exponents, 52* 32 * 42

Solution:

Since the powers are same , the sixth law can be used,

52* 32 * 42= (5*3*4)2

= (15*4)2

= (60)2

= 3600

**polynomials**, exponents, graphing, system of equations, logarithms, etc. Exponents are terms which is made up of two terms namely a base and superscript. The general format for exponents term is,z^m

where,

'z' is the base

'm' is the superscript

The various exponents law and examples for exponents used in math are given in the following sections.

**Laws for exponents in math:**The following

**laws of exponents**in math are very essential in solving exponents,1. The law for the product exponents with same base,

a^m * a^n = a^m+n, provided a`!=` b

2. The law for exponents with zero superscript,

a^0 = 1, provided a`!=` 0

3. The law for exponents in fraction form,

`a^m/a^n` = a^m * a^-n , provided a `!=` 0

4. The law for exponents with whole superscript,

(ab)m = a^m * b^m , provided a`!=` b

5.The law for exponents with negative superscript,

a-m = `1/a^m`provided a`!=` 0

I have recently faced lot of problem while learning

**Negative Exponent**But thank to online resources of math which helped me to learn myself easily on net.6. The law for exponents with common superscript when the terms are in product,

(a^m b^m c^m) = (a*b*c)^m ,

`(a^m/b^m)` = (`a/b` )^m , provided a`!=` b

7. The law for exponents with radicals,

`root(n)(x^m)` = x`m/n`

`8. The law for exponents to exponents,`

(a^m)^n= a^mn

**Math examples using laws of exponents:****Example 1:**Simplify the math expression using laws of exponents , 22 * 23 * 22

Solution:

Since the base of the expressions are same, we can use the first law from the list shown above,

a^m * a^n = a^m+n, provided a`!=` b

Therefore,

22 * 23 * 22 = (2)2+3+2

= 27

= 128

**Example 2:**Simplify the math expression using laws of exponents, `2^3 / 2^2`

Solution:

Using the exponents law three from the above listed laws,

`a^m/a^n` = a^m * a^-n , provided a `!=` 0

`2^3/2^2` = 23 *2-2

Using property 1 again,

= 23-2

= 2

**Example 3:**Simplify the math expression using laws of exponents, (53 / 53) * 50

Solution:

Since the base of the expressions are same, we can use the sixth law from the list laws shown above,

`5^3/5^3` *50 = 1 * 50

Using the property 2,

= 1 * 1

= 1

**Example 4:**Simplify the math expression using laws of exponents, 52* 32 * 42

Solution:

Since the powers are same , the sixth law can be used,

52* 32 * 42= (5*3*4)2

= (15*4)2

= (60)2

= 3600