Negative Fractional Exponent problem

In summary, a negative fractional exponent is a way of representing a number that is less than 1 and has a negative power. It can be solved by taking the reciprocal of the base number, changing the exponent to a positive one, and simplifying the resulting fraction. Negative fractional exponents can often be simplified using the rules of exponents. The main difference between a negative fractional exponent and a negative exponent is that the former represents a number between 0 and 1 while the latter represents a number raised to a negative power. Negative fractional exponents are useful because they allow for more efficient representation of numbers and follow the same rules as other exponents.
  • #1
jdoyle
7
0
Hi All,

Can anyone walk me through this problem. This is from an old med school entry test.

The answer is 81 but I can't work out how the x terms cancel.



3x(3x^ -1/3)^3

Thanks in advance

John
 
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  • #2
[tex]\frac{3x}{(^3\sqrt{x})^3}3^3=\frac{3x}{x}3^3=27*3=81[/tex]

Given of course that x is not 0.
 
  • #3
Hi Meldraft,

It looks so simple I don't know why I didn't do it that way. Thanks very much.

John
 
  • #4
It's very easy to put that 3^3 in the denominator by accident :wink:
 

FAQ: Negative Fractional Exponent problem

What is a negative fractional exponent?

A negative fractional exponent is a way of representing a number that is less than 1 and has a negative power. For example, 2-1/2 is equivalent to 1/√2. It is essentially the same as taking the reciprocal and then raising it to a positive power.

How do you solve a negative fractional exponent problem?

To solve a negative fractional exponent problem, you can follow these steps:

  1. Take the reciprocal of the base number.
  2. Change the negative exponent to a positive exponent by moving it to the numerator or denominator, depending on where it is located.
  3. Simplify the resulting fraction, if possible.
  4. Calculate the value of the new exponent.

Can a negative fractional exponent be simplified?

Yes, a negative fractional exponent can often be simplified by using the rules of exponents. For example, 2-3/4 can be simplified to 1/23/4 which is equivalent to 1/√8.

What is the difference between a negative fractional exponent and a negative exponent?

A negative fractional exponent represents a number that is less than 1 and has a negative power, while a negative exponent represents a number that is raised to a negative power. For example, 2-1 is equivalent to 1/2, while 2-1/2 is equivalent to 1/√2.

Why do we use negative fractional exponents?

Negative fractional exponents are useful because they allow us to represent numbers that are between 0 and 1 in a more compact and efficient way. They also follow the same rules as other exponents, making it easier to perform calculations involving these numbers.

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