How to go from 246 (2n) to (2^n)n

Thread starter mathbrah
Start date Oct 25, 2013

In summary, to simplify an expression like 2*4*6 (2n), you can use the power rule to add the exponents of the same base. To convert this expression to (2^n)n, you can use the commutative property of multiplication. The rule for simplifying expressions with exponents is the power rule, which can also be extended to dividing powers. Exponential growth occurs when the value of 2^n increases significantly as n increases. This expression can be used in real-world applications such as finance and population growth.

Oct 25, 2013

mathbrah

how would one see the first

and come up with the second

Physics news on Phys.org

Oct 25, 2013

SteamKing

Staff Emeritus

Science Advisor

Homework Helper

Have you tried factoring 2 from 2*4*6*...(2n)?

Oct 25, 2013

Mark44

Mentor

Insights Author

In the product 2 * 4 * 6 * ... * (2n), how many factors are explicitly shown there?

Oct 25, 2013

vanhees71

Science Advisor

Insights Author

Gold Member

2023 Award

I write it even a bit more explicitly
[tex]2 \cdot 4 \cdot 6 \cdots (2n)=(2 \cdot 1) \cdot (2 \cdot 2) \cdot (2 \cdot 3) \cdots (2n).[/tex]

Related to How to go from 246 (2n) to (2^n)n

1. How do you simplify an expression like 246 (2n)?

In order to simplify an expression like 2*4*6 (2n), you can use the power rule, which states that when multiplying powers with the same base, you can add the exponents. In this case, we can rewrite 2*4*6 (2n) as 2^1 * 2^2 * 2^3 * 2^n. Then, using the power rule, we can simplify this to 2^(1+2+3+n) = 2^(6+n).

2. How do you convert an expression from 246 (2n) to (2^n)n?

To convert an expression from 2*4*6 (2n) to (2^n)n, we can use the commutative property of multiplication, which states that the order of multiplication does not change the result. Therefore, we can rewrite the expression as 2^n * 2^(n+1) * 2^(n+2) = (2^n)^3 = (2^n)n.

3. What is the rule for simplifying expressions with exponents?

The rule for simplifying expressions with exponents is the power rule, which states that when multiplying powers with the same base, you can add the exponents. This can also be extended to dividing powers with the same base, where you can subtract the exponents.

4. Can you explain the concept of exponential growth in relation to this expression?

Exponential growth occurs when a quantity increases exponentially over time. In this expression, as the value of n increases, the value of 2^n also increases significantly. For example, when n=0, 2^n = 2^0 = 1. But when n=5, 2^n = 2^5 = 32. This shows that as n increases, the value of 2^n grows exponentially.

5. How can I use this expression in real-world applications?

This expression can be used in various real-world applications, such as in finance and population growth. In finance, it can be used to calculate compound interest, where n represents the number of compounding periods. In population growth, it can be used to model the growth of a population over time, where n represents the number of generations.