Questions: y=(4e^(6lnx)-3x^(2/3))

Solution Steps

To solve the given expression for $y$, we need to simplify the terms inside the parentheses. Specifically, we need to handle the exponential and logarithmic functions, as well as the power of $x$.

1. Simplify $4 e^{6 \ln x}$ using properties of exponents and logarithms.
2. Simplify $3 x^{2/3}$.
3. Combine the simplified terms to get the final expression for $y$.

Using the property of logarithms and exponents, $e^{\ln a} = a$, we can simplify $4 e^{6 \ln x}$ as follows: $$4 e^{6 \ln x} = 4 (e^{\ln x})^6 = 4 x^6$$

The term $3 x^{2/3}$ is already in its simplest form.

Now, we combine the simplified terms to get the final expression for $y$: $$y = 4 x^6 - 3 x^{2/3}$$

Final Answer