Product Law of Exponents
Introduction for exponents:
The exponents are means that, which the number is in power place of base number. And easy way to represent the exponents are, written as a small number to the right side and above of the base number. It is known as exponents. These exponents have some more important laws. Now we are going to explain about one of the important laws of exponents.
For example: 62, here 6 is the base number, and 2 is the exponent.
It is write it as 2 times of 6. Like (6 * 6)
If we have the variables, which is containing the exponents and have equal bases means, we can do some mathematical operations with them. Those operations are called as the “laws of exponents”
Example: Ax. Here A = base, and x = exponent.
Law of exponents types:
There are several laws are there in the law of exponents.
- Product law,
- Quotient law,
- Zero exponent law,
- Power law, and
- Rational exponent law and so on.
These all are the important law of exponents, but now we have to see about the Product law of exponents.
This product law of exponents is also known as first law of exponents. This law involves discovery methods.
If x>0 is a rational number and m and n are rational exponents, then
Product law of exponents is, Xm * Xn = X (m+n)
Here, m and n are real term values and X not equal to zero.
This product rule is applicable for, only when the base is same.
For example: 32 * 36
= 3(2+6)
= 38.
Example 1: a2 * a5 * a3
Solution:
= a2 * a5 * a3
= a (2+5+3)
= a10
Answer is: a10
Example 2: 3(2+3) * 3(3+2) * 3(7)
Solution:
= 3(2+3) * 3(3+2) * 3(7)
= 35 * 35 * 37
= 317
Answer is: 317
