%5E3-without-exponents.jpeg "(2n)^3 Without Exponents")
Understanding (2n)^3 without Exponents
The expression (2n)^3 might seem intimidating at first glance, especially if you're not comfortable with exponents. But fear not! We can break it down and express it without using any exponents.
The Basics of Exponents
Let's start by understanding what an exponent means. The exponent indicates how many times a base number is multiplied by itself. In our case, we have (2n)^3. This means we multiply (2n) by itself three times.
Expanding the Expression
Let's expand (2n)^3:
(2n)^3 = (2n) * (2n) * (2n)
Now, we need to remember the distributive property of multiplication. This means we multiply each term in the first set of parentheses by each term in the second set of parentheses, and so on.
- Step 1: Multiply the first two sets of parentheses:
(2n) * (2n) = (2 * 2) * (n * n) = 4n^2
- Step 2: Multiply the result from step 1 by the remaining set of parentheses:
4n^2 * (2n) = (4 * 2) * (n^2 * n) = 8n^3
The Final Result
Therefore, (2n)^3, expressed without exponents, is 8n^3.
Key Takeaway
By understanding the concept of exponents and using the distributive property, we can rewrite expressions like (2n)^3 without relying on exponents. This allows for a clearer understanding of the underlying multiplication involved.