Questions: x(7x-5)^(-4/5)+6(7x-5)^(1/5)

Solution Steps

To solve the expression \( x(7x-5)^{-\frac{4}{5}} + 6(7x-5)^{\frac{1}{5}} \), we need to evaluate it for a given value of \( x \). The expression involves exponents and requires careful handling of the power terms. We will use Python to substitute a specific value for \( x \) and compute the result.

We start by substituting \( x = 2 \) into the expression \( x(7x-5)^{-\frac{4}{5}} + 6(7x-5)^{\frac{1}{5}} \).

First, we calculate \( 7x - 5 \): \[ 7(2) - 5 = 14 - 5 = 9 \]

Now we evaluate each term in the expression:

1. For the first term: \[ x(7x-5)^{-\frac{4}{5}} = 2(9)^{-\frac{4}{5}} \]
2. For the second term: \[ 6(7x-5)^{\frac{1}{5}} = 6(9)^{\frac{1}{5}} \]

Next, we calculate the powers:

• \( (9)^{-\frac{4}{5}} \) and \( (9)^{\frac{1}{5}} \).

Finally, we combine the results of both terms: \[ 2(9)^{-\frac{4}{5}} + 6(9)^{\frac{1}{5}} \approx 9.6559 \]

Final Answer