Multiplication in exponential form involves expressing numbers with a common base as powers and then multiplying them. This is particularly useful when dealing with large or small numbers, as it simplifies calculations and representation. The general idea is to multiply the bases while adding the exponents. Let's break down the process step by step:
Suppose you have two numbers,
a and
b, both expressed in exponential form:
=
a=x
m
=
b=x
n
Here,
x is the common base, and
m and
n are the exponents associated with
a and
b respectively.
To multiply
a and
b, you can multiply their bases (
x) and add their exponents (
m and
n):
β
=
β
=
+
aβ
b=x
m
β
x
n
=x
m+n
So, when you multiply two numbers in exponential form with the same base, you add the exponents together and keep the base unchanged.
Here's an example:
Let's multiply
2
3
2
3
and
2
5
2
5
:
2
3
β
2
5
=
2
3
+
5
=
2
8
=
256
2
3
β
2
5
=2
3+5
=2
8
=256
In this example, we multiplied the bases (which are both 2) and added the exponents (3 and 5) to get the result in exponential form.
This property of multiplication with exponential notation holds true for any base, not just 2. As long as the bases are the same, you can multiply the numbers by adding their exponents.