Final answer:
To solve substitution of the exponent, apply the exponent to each term inside the parentheses and simplify the expression by combining the results.
Step-by-step explanation:
Solving Substitution of the Exponent
When we have an expression with substitution of the exponent, such as x^2 e^(4x^3), we need to understand that the exponent applies to everything inside the parentheses. In this case, the exponent is 4x^3 which means the expression inside the parentheses, x^3, is being cubed and multiplied by 4. We can simplify the expression by applying the exponent to each term inside the parentheses and combining the results.
So, x^2 e^(4x^3) can be simplified as x^2 * (x^3)^4 = x^2 * x^(12) = x^(2+12) = x^14.
Therefore, the simplified expression is x^14.