Questions: k(x)=(x-5)^(2/3)

Solution Steps

To solve for the function \( k(x) = (x-5)^{\frac{2}{3}} \), we need to evaluate this expression for a given value of \( x \). The expression involves raising the difference \( (x-5) \) to the power of \( \frac{2}{3} \), which is equivalent to taking the cube root of \( (x-5) \) and then squaring the result.

The function given is \( k(x) = (x-5)^{\frac{2}{3}} \). This involves taking the cube root of \( (x-5) \) and then squaring the result.

We substitute \( x = 8 \) into the function: \[ k(8) = (8-5)^{\frac{2}{3}} \]

First, calculate the difference: \[ 8 - 5 = 3 \] Then, raise the result to the power of \( \frac{2}{3} \): \[ 3^{\frac{2}{3}} \]

The expression \( 3^{\frac{2}{3}} \) can be interpreted as: \[ (3^{\frac{1}{3}})^2 \] Calculating the cube root of 3 and then squaring it gives approximately: \[ 3^{\frac{1}{3}} \approx 1.4422 \] \[ (1.4422)^2 \approx 2.080 \]

Final Answer