# college algebra

posted by .

factor...
(x+4)^-3/5+(x+4)^-1/5+(x+4)^1/5

Please explain the process used to solve this type of expression. Answer should be in equation form if that helps....

• college algebra -

consider a simpler case:
x^5 + 2x^3 + 5x^2

the common factor is x^2, that is, the power with the smallest exponent, so

x^2(x^3 + 2x + 5)
how did we get the terms inside ?
We subtracted the exponent of the common factor from the original exponent.

now to our question,
(x+4)^-3/5+(x+4)^-1/5+(x+4)^1/5
clearly the base of (x+4) becomes part of the common factor,
what is the smallest exponent ? it is -3/5
so (x+4)^(-3/5) is the common factor

(x+4)^(-3/5)[1 + (x+4)^(2/5) + (x+4)^(4/5)]

you can check this answer by expanding it, remember when multiplying powers we add the exponents

## Similar Questions

1. ### Algebra

Can you help me answer this equation? 1 1 __ - __ x+h x _______________________ h Your algebraic expression did not get printed out in a recognizable form. It is better is you use parentheses and brackets, and try to type it in a single

3. ### math,algebra

Can someone explain this to me plese: to factor a number you.... and then can you explain to me To factor an algebraic expression into prime factors means..... thanks This is how I would complete these two sentences. To factor a number, …
4. ### algebra

What is the difference between an equation and an expression?
5. ### algebra

Create a unique example of dividing a polynomial by a monomial and provide the simplified form. Explain, in complete sentences, the two ways used to simplify this expression and how you would check your quotient for accuracy. please …
6. ### math

Jane is taking a class and asks you to help her figure out what her last grade must be in the class to get a 85 in the class. She tells you the following calculation is used to find your final grade: 75+85+90+X ----------- > or …
7. ### College Algebra

The expression x^2-7 is not factorable using integer values. But the expression can be written in the form X^2-(Square root7)^2 enabling us to factor it as a “binomial” and its conjugate: (x+square root 7)(x-square root 7) Use …
8. ### ALGEBRA 2

Factor the given expression. Then use the zero product rule and the quadratic formula to solve the problem. There should be three solutions to the equation. x^3-2197 x= PLEASE, help me with this one problem I am stuck on! THANKS!
9. ### ALGEBRA 2

Factor the given expression. Then use the zero product rule and the quadratic formula to solve the problem. There should be three solutions to the equation. x^3-2197 x= PLEASE, help me with this one problem I am stuck on! THANKS!
10. ### Algebra 1

I've tried so hard on this and I'm completely hopeless, can somebody help me out?

More Similar Questions