# How to Calculate 3^2048: Step-by-Step Guide

• tsuwal
In summary, to prove the given equation, start by using the given answer of 3^2048. From there, use the formula a^2 - b^2 = (a-b)(a+b) with a = 2^2048 and b = 3^2048. Repeat this process with a = 2^1024 and b = 3^1024, and continue until the last pair on the left. This will result in (2-3)(2+3), giving a minus sign in the equation.
tsuwal

the answer is 3^2048. How do I get there?

Since you are given the answer, use that information!

You have to prove that
##(2+3)(2^2+3^2)\cdots(2^{2048} + 3^{2048}) + 2^{4096} - 3^{4096} = 0##
Now, think what you can do with ##2^{4096} - 3^{4096}## ...

i don't know, what can i do :S?

and the answer is not given, it's multiple choice

a2 - b2 = (a-b)(a+b)

next repeat with a = 21024 and b = 31024
etc.
At the end you will have (2-3)(2+3). Just be careful with the sign.

Last edited:
but i got a plus sign not a minus sign...

tsuwal said:
but i got a plus sign not a minus sign...
No, its a minus sign:
##(2+3)(2^2+3^2)\cdots(2^{2048} + 3^{2048}) + 2^{4096} - 3^{4096} = 0##
AlephZero was referring to the last pair on the left.

now i get it. thanks!

## 1. How do I calculate 3^2048?

To calculate 3^2048, you can use a calculator or a computer program. Simply enter "3^2048" into the calculator or program and it will give you the answer.

## 2. Can I calculate 3^2048 by hand?

Technically, yes, you can calculate 3^2048 by hand. However, it would be extremely time-consuming and prone to error. It is highly recommended to use a calculator or computer program for such large calculations.

## 3. What is the result of 3^2048?

The result of 3^2048 is a very large number, approximately 1.42 x 10^978. This is because 3 multiplied by itself 2048 times results in a very large number with 978 digits.

## 4. Can I simplify the calculation of 3^2048?

No, 3^2048 cannot be simplified any further. It is already in its simplest form.

## 5. Are there any tips for calculating 3^2048?

If you are using a calculator or computer program, make sure to double check your input to avoid any errors. It may also be helpful to break the calculation into smaller parts, such as calculating 3^1024 twice and then multiplying the results together.

• General Math
Replies
3
Views
2K
• Calculus and Beyond Homework Help
Replies
4
Views
638
• General Math
Replies
7
Views
2K
• Other Physics Topics
Replies
1
Views
3K
• General Math
Replies
1
Views
895
• General Math
Replies
8
Views
2K
Replies
1
Views
1K
• General Math
Replies
3
Views
2K
• General Math
Replies
4
Views
971
• General Math
Replies
2
Views
999
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "https://www.physicsforums.com/threads/how-to-calculate-3-2048-step-by-step-guide.667933/", "fetch_time": 1721724416000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2024-30/segments/1720763518029.81/warc/CC-MAIN-20240723072353-20240723102353-00840.warc.gz", "warc_record_offset": 803221744, "warc_record_length": 16408, "token_count": 835, "char_count": 2600, "score": 4.40625, "int_score": 4, "crawl": "CC-MAIN-2024-30", "snapshot_type": "latest", "language": "en", "language_score": 0.8987288475036621, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00034-of-00064.parquet"}