(x+40^-1/5-(x+4)^-6/5
the answer is 30
looks like some typos
is this supposed to be an equation?
I see no equal sign.
I have a feeling you meant:
(x+4)^(-1/5) - (x+4)^(-6/5)
remember we take out a common factor with its smallest exponent, so
= (x+4)^(-5/6) ( (x+4)^1 - 1)
= (x+3)/(x+4)^(5/6)
To simplify the expression (x + 40^(-1/5) - (x + 4)^(-6/5), we can follow the order of operations (PEMDAS/BODMAS) and simplification rules for exponents.
Let's break it down step by step:
Step 1: Simplify x + 40^(-1/5):
To simplify this term, we need to evaluate 40^(-1/5). The negative exponent indicates taking the reciprocal of the base raised to the positive exponent.
40^(-1/5) = 1/40^(1/5)
Now, we need to simplify 40^(1/5).
40^(1/5) is the fifth root of 40. So, we can rewrite it as:
40^(1/5) = (2^3 * 5)^(1/5) = (2^(3/5) * 5^(1/5))
Therefore, x + 40^(-1/5) can be simplified as:
x + (1/40^(1/5)) = x + (1/(2^(3/5) * 5^(1/5)))
Step 2: Simplify (x + 4)^(-6/5):
To simplify this term, we need to evaluate (x + 4)^(-6/5). Similar to the previous step, we'll simplify the expression inside the parentheses first.
(x + 4)^(-6/5) = (x + 4)^(-6/5)
Step 3: Combine the simplified terms:
Now we can simplify the whole expression by combining the terms we simplified in steps 1 and 2.
(x + 40^(-1/5) - (x + 4)^(-6/5) = x + (1/(2^(3/5) * 5^(1/5))) - (x + 4)^(-6/5)
And there you have it! The expression (x + 40^(-1/5) - (x + 4)^(-6/5) has been simplified to x + (1/(2^(3/5) * 5^(1/5))) - (x + 4)^(-6/5).