The Exponents Property
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 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
Understanding What are Exponents is always challenging for me but thanks to all math help websites to help me out.
The properties and examples for exponents are given in the following sections.
Properties of exponents:
The following properties are very essential in solving exponents,
1. Property for the product exponents with same base,
a^m * a^n = a^m+n, provided a`!=` b
2. Property for exponents with zero superscript,
a^0 = 1, provided a`!=` 0
3. Property for exponemts in fraction form,
`a^m/a^n` = a^m * a-n , provided a `!=` 0
4. Property for exponents with whole superscript,
(ab)^m = a^m * b^m , provided a`!=` b
5. Property for exponents with negative superscript,
a-m = `1/a^m`provided a`!=` 0
6. Property 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. Property for exponents with radicals,
`root(n)(x^m)` = x`m/n`
`8. Property for exponents to exponents,`
(a^m)^n= a^mn
Math is widely used in day to day activities watch out for my forthcoming posts on Laws of Exponents and neet examination I am sure they will be helpful.
Example involving exponents property:
Example 1:
Simplify the expression using exponents property, 5^2 * 5^3 * 5^2
Solution:
Since the base of the expressions are sa^me, we ca^n use the first property from the list shown above,
a^m * a^n = a^m+n, provided a`!=` b
Therefore,
5^2 * 5^3 * 5^2 = (5)^2+3+2
= 5^7
= 78125
Example 2:
Simplify the expression using exponents property, `5^3 / 5^2`
Solution:
Using the exponents property three from the above listed properties,
`a^m/a^n` = a^m * a^-n , provided a `!=` 0
`5^3 / 5^2` = 5^3 *5^-2
Using property 1 again,
= 5^3-2
= 5
Example 3:
Simplify the expression using exponents property, (5^3 / 5^3) * 5^0
Solution:
Since the base of the expressions are sa^me, we ca^n use the sixth property from the list shown above,
`5^3/5^3` *5^0 = 1 * 5^0
Using the property 2,
= 1 * 1
= 1
Example 4:
Simplify the expression using exponents property, 5^2* 3^2 * 4^2
Solution:
Since the powers are sa^me , the sixth property ca^n be used,
5^2* 3^2 * 4^2= (5*3*4)^2
= (15*4)^2
= (60)^2
= 3600
z^m
where,
'z' is the base
'm' is the superscript
Understanding What are Exponents is always challenging for me but thanks to all math help websites to help me out.
The properties and examples for exponents are given in the following sections.
Properties of exponents:
The following properties are very essential in solving exponents,
1. Property for the product exponents with same base,
a^m * a^n = a^m+n, provided a`!=` b
2. Property for exponents with zero superscript,
a^0 = 1, provided a`!=` 0
3. Property for exponemts in fraction form,
`a^m/a^n` = a^m * a-n , provided a `!=` 0
4. Property for exponents with whole superscript,
(ab)^m = a^m * b^m , provided a`!=` b
5. Property for exponents with negative superscript,
a-m = `1/a^m`provided a`!=` 0
6. Property 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. Property for exponents with radicals,
`root(n)(x^m)` = x`m/n`
`8. Property for exponents to exponents,`
(a^m)^n= a^mn
Math is widely used in day to day activities watch out for my forthcoming posts on Laws of Exponents and neet examination I am sure they will be helpful.
Example involving exponents property:
Example 1:
Simplify the expression using exponents property, 5^2 * 5^3 * 5^2
Solution:
Since the base of the expressions are sa^me, we ca^n use the first property from the list shown above,
a^m * a^n = a^m+n, provided a`!=` b
Therefore,
5^2 * 5^3 * 5^2 = (5)^2+3+2
= 5^7
= 78125
Example 2:
Simplify the expression using exponents property, `5^3 / 5^2`
Solution:
Using the exponents property three from the above listed properties,
`a^m/a^n` = a^m * a^-n , provided a `!=` 0
`5^3 / 5^2` = 5^3 *5^-2
Using property 1 again,
= 5^3-2
= 5
Example 3:
Simplify the expression using exponents property, (5^3 / 5^3) * 5^0
Solution:
Since the base of the expressions are sa^me, we ca^n use the sixth property from the list shown above,
`5^3/5^3` *5^0 = 1 * 5^0
Using the property 2,
= 1 * 1
= 1
Example 4:
Simplify the expression using exponents property, 5^2* 3^2 * 4^2
Solution:
Since the powers are sa^me , the sixth property ca^n be used,
5^2* 3^2 * 4^2= (5*3*4)^2
= (15*4)^2
= (60)^2
= 3600