Final answer:
The given expression simplifies to 6.4 × 10^4 when expressed in scientific notation by multiplying the coefficients and applying the laws of exponents to the powers of ten.
Step-by-step explanation:
We need to write the given expression in scientific notation. The expression we have is (8 × 102) × (3.2 × 105) ÷ (4 × 103). We will first multiply and divide the coefficients (the numbers in front of the powers of 10) and then do the same for the powers of 10 using the laws of exponents.
Multiplying the coefficients:
8 × 3.2 = 25.6
Now, we manage the powers of ten using the exponent rules. When we multiply powers of 10 with the same base, we add their exponents:
102 × 105 but we also need to divide by 103, so we subtract 3 from the exponent:
102 + 5 - 3 = 104
Getting back to our coefficients, we now have:
25.6 ÷ 4 = 6.4
Combining the coefficients and the powers of 10, we get:
6.4 × 104
So the final result in scientific notation is 6.4 × 104.