Introduction for exponents:
The exponents are which integer is placed in the power of base numbers. It can be easily represent as, that is a small number to the right side and above of base number. It is called as exponents. In this exponents have many types. Rational exponents are one of the types of exponents. These rational exponents have some of important rules and laws. In this rules and laws are called as properties. In article we are going to explain about the important properties of exponents.
Explanatory for Rational Exponents:
Rational exponents are nothing but, it is one type of exponents. These exponents are in fraction form. Otherwise the power values raised to fraction. It is known as rational exponents.
Types of rational exponents properties:
There are seven important rules or properties are there, but here we have to given five important properties only. There are given below,
Properties of multiplying powers,
Power of quotient properties,
Power of product properties,
Power of power properties, and
Power of zero properties.
These all are the important properties of the rational exponents.
Between, if you have problem on these topics Descriptive Statistic, please browse expert math related websites for more help on Relation and Function.
Properties Explanations and Examples:
1. Properties of multiplying powers:
In this term the base numbers have same values and exponents only different. In this multiplying term, we will add the power values and take the base value as same.
It can be denoted as, xm * xn = xm+n.
2. Power of quotient rules:
In this term the base numbers have two different numbers and only one power for both base numbers. Then we will separate and write it as, (x/y) m = xm / ym.
3. Power of product properties:
This term will be having two different bases, but only one power value. And it can be denoted as, (xy) m = xm * ym.
4. Power of power properties:
In this power of power properties has only one base number, and having the one power value. Then whole value has one more power value. It is denoted as, (xm) n = xmn.
5. Power of zero properties:
This power of zero properties has any one base number with the power of zero values only. It can be getting constant answer is 1. It can be denoted as x0 = 1.
Example Problems in Properties of Rational Exponents:
1. Simplify: `(9)^ (2/3) * (9)^ (3/2)`
Solution:
Given: `(9)^ (2/3) * (9)^ (3/2)`
Use the property of multiplying powers, and write the expression,
= `(9)^ (2/3) * (9)^ (3/2)` = `9^ ((2/3) + (3/2))`
The LCD of exponents is `6` . So,
=` (9)^ ((4/6) + (9/6))`
= `(9)^ (13/6)`
Simplify the radicand, and we get
= `(3^2)^ (13/6)` .
Here we use the power of power property, and simplify, and we get
= `((3)^ (2)) ^ (13/6)`
= `(3) ^ (13/3)` .
Answer is `(3) ^ (13/3)` .
2. Factor the number into the square of another number and then simplify `196^-(1/2)`
Solution:
Given:` 196^-(1/2)`
Take the square root value,
=` (14^2) ^ - (1/2)`
Here we use the power of power property, and simplify
= `(14 ^2)^ (-(1/2))`
= `(14) ^ (-1)`
= `(14/1) ^ -1`
Here we use the power of quotient property,
= `(1/14) ^1`
= `1/14.`
Answer is `1/14` .
Those above explanations and examples problems makes this properties of exponents will clear.
The exponents are which integer is placed in the power of base numbers. It can be easily represent as, that is a small number to the right side and above of base number. It is called as exponents. In this exponents have many types. Rational exponents are one of the types of exponents. These rational exponents have some of important rules and laws. In this rules and laws are called as properties. In article we are going to explain about the important properties of exponents.
Explanatory for Rational Exponents:
Rational exponents are nothing but, it is one type of exponents. These exponents are in fraction form. Otherwise the power values raised to fraction. It is known as rational exponents.
Types of rational exponents properties:
There are seven important rules or properties are there, but here we have to given five important properties only. There are given below,
Properties of multiplying powers,
Power of quotient properties,
Power of product properties,
Power of power properties, and
Power of zero properties.
These all are the important properties of the rational exponents.
Between, if you have problem on these topics Descriptive Statistic, please browse expert math related websites for more help on Relation and Function.
Properties Explanations and Examples:
1. Properties of multiplying powers:
In this term the base numbers have same values and exponents only different. In this multiplying term, we will add the power values and take the base value as same.
It can be denoted as, xm * xn = xm+n.
2. Power of quotient rules:
In this term the base numbers have two different numbers and only one power for both base numbers. Then we will separate and write it as, (x/y) m = xm / ym.
3. Power of product properties:
This term will be having two different bases, but only one power value. And it can be denoted as, (xy) m = xm * ym.
4. Power of power properties:
In this power of power properties has only one base number, and having the one power value. Then whole value has one more power value. It is denoted as, (xm) n = xmn.
5. Power of zero properties:
This power of zero properties has any one base number with the power of zero values only. It can be getting constant answer is 1. It can be denoted as x0 = 1.
Example Problems in Properties of Rational Exponents:
1. Simplify: `(9)^ (2/3) * (9)^ (3/2)`
Solution:
Given: `(9)^ (2/3) * (9)^ (3/2)`
Use the property of multiplying powers, and write the expression,
= `(9)^ (2/3) * (9)^ (3/2)` = `9^ ((2/3) + (3/2))`
The LCD of exponents is `6` . So,
=` (9)^ ((4/6) + (9/6))`
= `(9)^ (13/6)`
Simplify the radicand, and we get
= `(3^2)^ (13/6)` .
Here we use the power of power property, and simplify, and we get
= `((3)^ (2)) ^ (13/6)`
= `(3) ^ (13/3)` .
Answer is `(3) ^ (13/3)` .
2. Factor the number into the square of another number and then simplify `196^-(1/2)`
Solution:
Given:` 196^-(1/2)`
Take the square root value,
=` (14^2) ^ - (1/2)`
Here we use the power of power property, and simplify
= `(14 ^2)^ (-(1/2))`
= `(14) ^ (-1)`
= `(14/1) ^ -1`
Here we use the power of quotient property,
= `(1/14) ^1`
= `1/14.`
Answer is `1/14` .
Those above explanations and examples problems makes this properties of exponents will clear.
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