Simplifying Exponential Expressions: 3^-6 x (3^4 / 3^0)^2
In this article, we will explore how to simplify the exponential expression 3^-6 x (3^4 / 3^0)^2. To do this, we need to understand the rules of exponents and how to apply them correctly.
Rule of Exponents: Product of Powers
The first rule we need to recall is the product of powers, which states that:
a^m × a^n = a^(m+n)
This rule allows us to multiply two exponential expressions with the same base by adding their exponents.
Simplifying the Expression
Let's start by simplifying the expression inside the parentheses:
(3^4 / 3^0)^2
Using the rule of exponents, we know that:
3^0 = 1
So, the expression becomes:
(3^4 / 1)^2
Now, we can simplify the fraction:
(3^4)^2
Using the power of a power rule, which states that:
(a^m)^n = a^(mn)
We can rewrite the expression as:
3^(4×2) = 3^8
Now that we have simplified the expression inside the parentheses, we can rewrite the original expression as:
3^-6 × 3^8
Simplifying the Final Expression
Using the product of powers rule, we can simplify the final expression by adding the exponents:
3^(-6 + 8)
3^2
9
Therefore, the simplified expression is:
9
In conclusion, by applying the rules of exponents, we were able to simplify the expression 3^-6 x (3^4 / 3^0)^2 to 9.
