%5E2-without-exponents.jpeg "(4n)^2 Without Exponents")
Understanding (4n)^2 without Exponents
The expression (4n)^2 represents the square of the quantity (4n). To understand this without exponents, we need to break it down into its fundamental meaning.
What is Squaring?
Squaring a number means multiplying it by itself. For example, 5 squared (5^2) is the same as 5 * 5 = 25.
Applying it to (4n)^2
Therefore, (4n)^2 is the same as (4n) * (4n).
Expanding the Expression
Now, let's expand this multiplication using the distributive property:
- (4n) * (4n) = (4 * 4) * (n * n)
Simplifying the Result
Finally, we simplify the expression:
- (4 * 4) * (n * n) = 16 * n^2
Therefore, (4n)^2 without exponents is equivalent to 16n^2.
Key Points
- Squaring a quantity means multiplying it by itself.
- The distributive property helps us expand multiplications.
- Understanding the basics of exponents and algebraic manipulation allows us to rewrite expressions in different forms.