A Number to a fraction of a power

In summary, the conversation discusses the concept of raising a number to a fractional power, specifically 125 to the power of 2/3. It is clarified that this means finding a number x that, when raised to the power of 3, equals 125 raised to the power of 2. Alternatively, the numerical answer is given as 25.
  • #1
AZTarzan
1
0
What is

125 to the power of 2/3

I think it is 1/125 or .008 but I'm not sure
 
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  • #2
What is the meaning of this question? Are you asking about the nature/significance of a number raised to a fractional power or are you actually looking for the numerical answer to 125^(2/3) ?!?

If the former, the answer is solving for x in the equation [itex]125^{2/3}=x[/itex], which is equivalent to the equation [itex]125^2 = x^3[/itex], which means finding the number x such that raised to the power 3 equal 125 raised to the power 2.

If the later, any calculator, even the cheapest, will tell you it's 25.
 
Last edited:
  • #3
just to clarify

125 to the power of 2/3

125^(2/3)

the /3 means the third or cube root and the 2 can be taken to mean squared
ince both are powers the Cube[(125^2)] will give you the answer.

hope this makes it clear!
 

1. What is a number to a fraction of a power?

A number to a fraction of a power is a mathematical expression that represents a number raised to a power that is a fraction. It is a way to express numbers in a more compact form, and is often used in scientific and engineering calculations.

2. How do you convert a number to a fraction of a power?

To convert a number to a fraction of a power, you can use the formula x^(a/b) = (x^(1/b))^a. This means that you take the bth root of x, and then raise it to the power of a. For example, to convert 16 to the 1/2 power, you would take the square root of 16 (which is 4), and raise it to the power of 1, giving you an answer of 4.

3. What is the purpose of using a number to a fraction of a power?

The purpose of using a number to a fraction of a power is to simplify complex expressions and make calculations more efficient. It is also used in scientific notation to represent very large or very small numbers in a more concise way.

4. Can any number be raised to a fraction of a power?

Yes, any number can be raised to a fraction of a power. This includes whole numbers, decimals, and irrational numbers. However, the resulting value may be a complex number or undefined in some cases.

5. How is a number to a fraction of a power different from a number to a whole number power?

The main difference between a number to a fraction of a power and a number to a whole number power is that the former results in a non-integer value, while the latter results in an integer value. Additionally, the rules for calculating and simplifying these expressions are different.

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