Pulling fractional exponents out of an expression

In summary, the conversation discusses finding the critical numbers of the function F(t) = t^(3/4) - 2t^(1/4) and manipulating fractional exponents in the process. The derivative is rewritten as F'(t) = (1/4)t^(-3/4)[3t^(1/2) - 2) and it is advised to use parentheses or LaTeX when writing exponents to avoid confusion.
  • #1
Cjosh
6
0

Homework Statement


Find critical numbers of the function: F(x)=t^3/4 - 2t^1/4
Derivative I got: F'(x)=3/4 t^-1/4 - 1/2 t^-3/4

Homework Equations

The Attempt at a Solution


I have found the derivative and I understand I must pull out a t in order to find critical numbers, and run across this issue of manipulating fractional exponents too often. How do I go about this? Thankyou.
 
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  • #2
Please post questions about calculus problems in the Calculus & Beyond section, not in the Precalculus section. I have moved your post.
Cjosh said:

Homework Statement


Find critical numbers of the function: F(x)=t^3/4 - 2t^1/4
Derivative I got: F'(x)=3/4 t^-1/4 - 1/2 t^-3/4
First off -- your two functions are functions of t, not x, so they should be written as F(t) and F'(t).

Cjosh said:

Homework Equations

The Attempt at a Solution


I have found the derivative and I understand I must pull out a t in order to find critical numbers, and run across this issue of manipulating fractional exponents too often. How do I go about this? Thankyou.
Rewrite the derivative so that it is a product rather than a sum. In this case, factor t^(-3/4) out of both terms.
 
  • #3
Mark44 said:
Please post questions about calculus problems in the Calculus & Beyond section, not in the Precalculus section. I have moved your post.
First off -- your two functions are functions of t, not x, so they should be written as F(t) and F'(t).Rewrite the derivative so that it is a product rather than a sum. In this case, factor t^(-3/4) out of both terms.

So from this I get F'(t)= t^-3/4 (3/4t^1/2 - 1/2)
 
  • #4
Cjosh said:
So from this I get F'(t)= t^-3/4 (3/4t^1/2 - 1/2)
Yes, that's correct, but even better is F'(t) = (1/4)t^(-3/4)[3t^(1/2) - 2)
Note that when you write exponents as inline text, t^-3/4 is usually interpreted as ##\frac{t^{-3}} 4##, using the usual rules of precedence.

This site supports the use of LaTeX (see https://www.physicsforums.com/help/latexhelp/ under the INFO menu, in Help/How-to articles).
Using LaTeX, the derivative looks like this:
$$F'(t) = \frac 1 4 t^{-3/4}(3t^{1/2} - 2)$$
 
  • #5
Cjosh said:

Homework Statement


Find critical numbers of the function: F(x)=t^3/4 - 2t^1/4
Derivative I got: F'(x)=3/4 t^-1/4 - 1/2 t^-3/4

Homework Equations

The Attempt at a Solution


I have found the derivative and I understand I must pull out a t in order to find critical numbers, and run across this issue of manipulating fractional exponents too often. How do I go about this? Thankyou.

What you wrote means ##F = \frac{1}{4} t^3 - \frac{2}{4} t^1##. If you mean ##F = t^{3/4} - 2 t^{1/4}##, then you must use parentheses (or else use LaTeX, as I just did). With parentheses you would have F = t^(3/4) - 2 t^(1/4).
 

Related to Pulling fractional exponents out of an expression

1. What is the purpose of pulling fractional exponents out of an expression?

Pulling fractional exponents out of an expression allows us to simplify the expression and make it easier to work with. It also helps us to better understand the relationship between the different parts of the expression.

2. Can fractional exponents be pulled out of any type of expression?

Yes, fractional exponents can be pulled out of any expression that contains terms with exponents. This includes expressions with variables, constants, and operations such as addition, subtraction, multiplication, and division.

3. How do you pull fractional exponents out of an expression?

To pull fractional exponents out of an expression, we use the properties of exponents. Specifically, we use the property that (a^m)^n = a^(mn). This allows us to move the exponent from the base to the coefficient, or vice versa.

4. Are there any rules or limitations when pulling fractional exponents out of an expression?

Yes, there are a few rules and limitations to keep in mind. First, the fractional exponent must be in the form of a fraction with a numerator and denominator. Additionally, the exponent cannot be pulled out if it results in a negative exponent. Lastly, the expression must have a common base for the fractional exponent to be pulled out.

5. How do pulling fractional exponents out of an expression help in solving equations?

Pulling fractional exponents out of an expression can help us solve equations by simplifying the expression and making it easier to work with. This can then lead to easier factoring, substitution, and other techniques used in solving equations. It also allows us to see the relationship between different parts of the expression and determine the best approach for solving the equation.

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