As for the question,How can I simplify (8x^1/2)/(x^2/3)]^1/3?

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In summary, the conversation discusses the simplification of the expression [(8x^1/2)/(x^2/3)]^1/3, with the final answer being 2/x^1/18. The conversation also touches on the steps involved in simplifying the expression, including converting rational exponents to a common denominator.
  • #1
Alex6977
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Hi i have a question i know the answer to but don't understand how it was reached.

[(8x^1/2)/(x^2/3)]^1/3

it comes to 2/x^1/18
but how? I got 8/x^1/18

thx
 
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  • #2
Re: Simplificaiton issues

Hello and welcome! :D

$$\left(\frac{8x^{1/2}}{x^{2/3}}\right)^{1/3}=\left(\frac{8}{x^{1/6}}\right)^{1/3}=\frac{8^{1/3}}{\left(x^{1/6}\right)^{1/3}}=\frac{2}{x^{1/18}}$$
 
  • #3
Re: Simplificaiton issues

I see i tried applying the outside ^1/3 first to eliminate that right off the bat. which would be

8x^1/6 over X^2/9.

but that's still corrrect so far right?

then that equals.

8x^3/18 over x^4/18. but then it starts to look bad and i get lost. maybe you just can't do it that way?

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Oh and thanks
 
  • #4
Your first step is valid, you just need to remember to apply it to the 8 as well, so that you have:

\(\displaystyle \left(\frac{8x^{1/2}}{x^{2/3}}\right)^{1/3}=\frac{2x^{1/6}}{x^{2/9}}\)

Your next step is good too, to convert the rational exponents to a common denominator so they can be subtracted:

\(\displaystyle \left(\frac{8x^{1/2}}{x^{2/3}}\right)^{1/3}=\frac{2x^{3/18}}{x^{4/18}}=\frac{2}{x^{1/18}}\)
 
  • #5
I can't follow that. sorry

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nevermind its displaying right now

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AHHHHH i didn't apply it to the 8. THere we go. Thanks a ton
 
  • #6
Alex6977 said:
I can't follow that. sorry

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nevermind its displaying right now

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AHHHHH i didn't apply it to the 8. THere we go. Thanks a ton

Yeah, I had some missing brackets in my $\LaTeX$ code, and I didn't preview, so you saw a real mess before I got it fixed. :D
 

FAQ: As for the question,How can I simplify (8x^1/2)/(x^2/3)]^1/3?

What is simplification and why is it important in science?

Simplification is the process of reducing complex systems or concepts into simpler and more manageable forms. It is important in science because it allows scientists to better understand and analyze complex phenomena, make accurate predictions, and communicate their findings more effectively.

How do scientists decide which aspects to simplify in their research?

Scientists use their knowledge and expertise to identify the most important and relevant aspects of a system or concept to focus on, while disregarding less significant details. They may also use mathematical and statistical techniques to determine which variables have the greatest impact on the overall system.

What are the potential limitations of simplification in scientific research?

While simplification can be useful in understanding complex phenomena, it can also lead to oversimplification and potentially overlook important details or variables. This can result in inaccurate conclusions and predictions. Additionally, simplification may not always be appropriate in certain areas of research, such as in highly specialized and complex fields.

How can scientists ensure that their simplifications are accurate and reliable?

Scientists can use a variety of methods to validate their simplifications, such as conducting experiments, collecting data, and using mathematical models. They can also collaborate with other experts in the field to review and critique their simplifications and ensure their accuracy.

Can simplification be applied to all scientific disciplines?

While simplification is commonly used in many scientific disciplines, it may not be suitable for all areas of research. Some disciplines, such as theoretical physics, may require more complex and nuanced approaches. It is important for scientists to carefully consider the appropriateness of simplification in their specific field of study.

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