(x+40)^-1/5-(x+4)^-6/5
i say the answer is 32
assuming a typo and either x+40 is supposed to be x+4, or vice versa,
u^-1/5 - u^-6/5
= u^-1/5 (1-1/u)
= (x+4)^-1/5 * (x+3)/(x+4)
Not sure where you want to go with this. Take it over to wolframalpha.com and it will give you several different ways to write it.
To simplify the expression (x+40)^(-1/5) - (x+4)^(-6/5), we need to work with the negative exponents first.
Let's rewrite the expression using positive exponents:
(x+40)^(-1/5) - (x+4)^(-6/5) = 1/(x+40)^(1/5) - 1/(x+4)^(6/5)
Now, to simplify this expression further, we can find a common denominator. The common denominator can be found by raising each denominator to the power of the least common multiple of the exponents, which in this case is 5.
So, we rewrite the expression with the common denominator:
= (1/(x+40)^(1/5))(x+4)^(5/5) - (1/(x+4)^(6/5))(x+40)^(5/5)
Simplifying this further, we get:
= (x+4)/(x+40) - (x+40)/(x+4)^(6/5)
Next, we can simplify the denominators:
= (x+4)/(x+40) - (x+40)/((x+4)^(6/5))^(5/5)
Now, we can raise the denominator of the second term to the power of 6:
= (x+4)/(x+40) - (x+40)/((x+4)^6)^(1/5)
Finally, we have simplified the expression to:
= (x+4)/(x+40) - 1/(x+4)^5