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EXPONENTS OF REAL NUMBERS
exponents OR index or index number or power
If a number is multiplied by itself a number of times, then it can be written in the exponential form 3 × 3 = 32 O R x × x × x × .... n times = xn
LAWS OF INTEGRAL EXPONENTS
First law (Product Law):- Let a be any real number and m, n are positive integers, then
RATIONAL EXPONENTS OF A REAL NUMBER
Principal nth root of a Positive real number:- Let a be a positive real number and n be a positive integer. Then, the principal nth root of a is the unique positive real number x such that xn = a.
The principal nth root of a positive real number a is denoted by 
LAWS OF EXPONENTS
Let a, b > 0 be a real number, and let m and n be rational numbers.
Then, we have
Ex. Evaluate each of the following:-
|
x = any positive real number m = an integer n = natural number Index of a radical is always a positive integer. |
Here, xm is called the Radicand
n is called the index of the radical
|
is called a radical
sign is called the radical signFAQs on Laws of Exponents for Real Numbers - Number Systems, Class 9, Mathematics
| 1. What are the laws of exponents for real numbers? |  |
Ans. The laws of exponents for real numbers are rules that simplify the multiplication, division, and powers of real numbers. These laws are:
1. Product Law: a^m × a^n = a^(m+n)
2. Quotient Law: a^m ÷ a^n = a^(m-n)
3. Power Law: (a^m)^n = a^(m×n)
4. Negative Exponent Law: a^(-n) = 1/a^n
5. Zero Exponent Law: a^0 = 1
| 2. How can I simplify expressions using the laws of exponents? | |
Ans. To simplify expressions using the laws of exponents, you need to apply the appropriate law depending on the given expression. For example, if you have to simplify 2^3 × 2^4, you can use the product law to get 2^(3+4) = 2^7. Similarly, if you have to simplify (3^4)^2, you can use the power law to get 3^(4×2) = 3^8.
| 3. Can the laws of exponents be applied to all real numbers? | |
Ans. Yes, the laws of exponents can be applied to all real numbers, including negative numbers, fractions, decimals, and irrational numbers.
| 4. How do I know which law of exponents to use for a given expression? | |
Ans. You need to identify the operation (multiplication, division, or power) and the properties (positive, negative, zero) of the given numbers in the expression. Once you have identified these, you can apply the appropriate law of exponents.
| 5. Why is it important to learn the laws of exponents? | |
Ans. The laws of exponents are fundamental rules that simplify and solve complex mathematical problems involving real numbers. They are essential in algebra, calculus, and other advanced mathematical concepts. Understanding and applying these laws can help you solve problems quickly and efficiently, and build a strong foundation for further mathematical studies.
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