Final answer:
To simplify the given expression, calculate 3^5 and 2^2 separately, sum them up, and then multiply the result by 2^4. The step-by-step process includes evaluating integer powers and performing addition and multiplication to reach the final answer of 3952.
Step-by-step explanation:
The expression given is 2^4 * (3^5 + 2^2). In order to simplify this expression, we need to address the operation inside the parentheses first. The exponential terms 3^5 and 2^2 represent integer powers, meaning 3^5 is 3 multiplied by itself 5 times and 2^2 is 2 multiplied by itself twice.
To solve for 3^5, one would calculate 3*3*3*3*3. Similarly, to solve for 2^2, the calculation is 2*2. Therefore, 3^5 is 243 and 2^2 is 4. Adding these together yields 247. The next step is to multiply this sum by 2^4, which is 16 (since 2^4 is 2*2*2*2).
Finally, we multiply 16 by 247 to find the final answer. In summary, the steps are:
- Calculate 3^5 = 243
- Calculate 2^2 = 4
- Add 243 and 4 to get 247
- Calculate 2^4 = 16
- Multiply 16 by 247 to get the final answer, 3952