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