How do I simplify (v/pi)(2pi/v)2/3 to 2(v/2pi)1/3?

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In summary, the conversation discusses how to simplify the expression (v/pi)(2pi/v)2/3 and determine if it is equal to 2(v/2pi)1/3. The solution is found to be correct and it is confirmed by another member.
  • #1
JOhnJDC
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Homework Statement



Please help me understand how (v/pi)(2pi/v)2/3 equals 2(v/2pi)1/3

This is from my book.

The Attempt at a Solution



[(v)(22/3)(pi2/3)]/v2/3pi = 22/3(v/pi)1/3

What am I doing wrong? Thanks.

EDIT: I made a mistake in copying over my attempt; fixed now.
 
Last edited:
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  • #2
I'm beginning to think that my book is wrong and that my attempt is correct. Can anyone confirm?
 
  • #3
You are both correct :wink:
 
  • #4
Mentallic said:
You are both correct :wink:

I don't see how 22/3(v/pi)1/3 = 2(v/2pi)1/3 Can you explain?
 
Last edited:
  • #5
[tex]2^{2/3}=2^{1-1/3}[/tex]

does it seem obvious now?
 
  • #6
Mentallic said:
[tex]2^{2/3}=2^{1-1/3}[/tex]

does it seem obvious now?

Yes--I see it now. Thanks, Mentallic.
 

FAQ: How do I simplify (v/pi)(2pi/v)2/3 to 2(v/2pi)1/3?

What is an exponent?

An exponent is a mathematical notation that indicates the number of times a base number is multiplied by itself. It is written as a superscript to the right of the base number, such as 23 (read as "2 to the power of 3"). This means that 2 is multiplied by itself 3 times, resulting in the value of 8.

What is a radical?

A radical is a mathematical symbol (√) used to denote the square root of a number. It can also represent higher order roots, such as cube roots (∛) or fourth roots (∜). For example, √9 = 3, ∛27 = 3, and ∜16 = 2.

What is the difference between an exponent and a radical?

Exponents and radicals are inverse operations of each other. While an exponent indicates repeated multiplication, a radical indicates the inverse operation, or the number that was multiplied to get the result. For example, 32 = 9, and √9 = 3.

How do I simplify expressions with exponents and radicals?

To simplify expressions with exponents and radicals, you can apply the properties of exponents and radicals. These include the product rule, quotient rule, power rule, and root rule. It is also helpful to know the basic rules of arithmetic, such as the order of operations, and how to combine like terms.

What are some real-world applications of exponents and radicals?

Exponents and radicals are used in various fields of science, such as physics, chemistry, and engineering, to represent exponential growth and decay, as well as the square root and cube root laws. They are also used in financial calculations, such as compound interest and mortgage payments, and in computer programming for calculations and data compression.

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