Final answer:
2 to the power of 16 equals 65,536. This involves multiplying 2 by itself 16 times, which can also be expressed in scientific notation as 6.5536 x 10^4.
Step-by-step explanation:
The student has asked to calculate 2 to the power of 16. To find this, we perform an exponentiation, which means multiplying 2 by itself 16 times. It can be challenging to perform this calculation in our heads, but we can simplify the process by using properties of exponents. Squaring of exponentials involves squaring the base number and then understanding how to handle positive and negative exponents.
Another useful skill is handling exponents in scientific notation, such as understanding that 2.4 x 10-2 results in moving the decimal place two positions to the left to get 0.024. Furthermore, when multiplying numbers with exponents, like in scientific notation, we add the exponents; and when dividing, we subtract the exponents of the powers of ten.
To answer the student's question directly, 2 to the power of 16 is equal to 65,536, which can also be represented in scientific notation as 6.5536 x 104.