Simplifying Exponents: Tips and Tricks for Solving Complex Equations

In summary, the conversation is about a math problem involving finding the value of f(g(x)), where f(x) is equal to 1 over the square root of x and g(x) is equal to x squared minus 5. The person asking the question is confused about the correct approach and mentions being used to using a calculator for math problems.
  • #1
dustinj.11
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Homework Statement



Attached is the problem, I don't like the math editor used on this site, so its a pdf. The only real problem I have is how to is how do you square a problem like square root of x over 2x?
 

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  • #2
dustinj.11 said:

Homework Statement



Attached is the problem, I don't like the math editor used on this site, so its a pdf. The only real problem I have is how to is how do you square a problem like square root of x over 2x?

Welcome to the PF.

Since you are given [tex]f(x) = \frac{1}{\sqrt{x}}[/tex]

and [tex]g(x) = x^2 - 5[/tex]

what is f(g(x))? Wouldn't you substitute the g(x) term into the f(x) equation? Where do you get "square root of x over 2x"?
 
  • #3
Thanks for the help, bt the answers were multiple choice, and as it turns out the correct choice wasn't there. Thats what confused me. Sorry if i seemed a little confused, just I was bred on a calculator, and now my calc ab teacher won't let us use any type of calculator. So, 90% of the time my brain is fried.
 

FAQ: Simplifying Exponents: Tips and Tricks for Solving Complex Equations

What are exponents?

Exponents are mathematical notation used to represent repeated multiplication of a number, also known as powers. They are written in the form of a superscript number above the base number, such as 23 (read as "2 to the power of 3").

How do I simplify expressions with exponents?

To simplify expressions with exponents, you can use the rules of exponents. These include the product rule, quotient rule, power rule, negative exponent rule, and zero exponent rule. By applying these rules, you can reduce complex expressions to simpler forms.

What is the difference between a base and an exponent?

The base is the number being multiplied repeatedly, while the exponent represents the number of times the base is multiplied by itself. For example, in 53, 5 is the base and 3 is the exponent.

How can I solve equations with exponents?

To solve equations with exponents, you can use the properties of exponents to simplify the expression. Then, you can use algebraic techniques such as combining like terms, distributing, and isolating variables to solve for the unknown variable.

Can exponents be negative or fractions?

Yes, exponents can be negative or fractions. A negative exponent indicates that the base is in the denominator of a fraction, while a fraction exponent indicates that the root of the base is being taken. For example, 4-2 = 1/42 = 1/16.

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