Final answer:
To simplify the expression e^(ln(z^4) + 3ln(y)), we can use the properties of logarithms and exponents to rewrite it as z^4y^3.
Step-by-step explanation:
To simplify the expression e^(ln(z^4) + 3ln(y)), we can use the properties of logarithms and exponents. First, using the property that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number, we can rewrite the expression as e^(4ln(z) + 3ln(y)). Next, we can use the property that the logarithm of a product of two numbers is the sum of the logarithms of the two numbers, which gives us e^(ln(z^4) * 3ln(y)). Finally, using the property that the exponent of an exponential term can be multiplied by a constant, we can simplify the expression to e^(ln(z^4y^3)). Since the exponential function and logarithm function are inverses of each other, the logarithm and exponential cancel out, leaving us with the simplified expression of z^4y^3.