Final answer:
To solve 8^6 divided by 8, we subtract the exponent of the divisor (8^1) from the dividend (8^6), resulting in 8^5, which equals 32,768. For dividing powers of 10, you subtract the lower exponent from the higher one and simplify the coefficients separately.
Step-by-step explanation:
To solve 8^6 divided by 8, we can use the exponent rule that states when we divide two powers with the same base, we subtract the exponents. Thus,
8^6 ÷ 8 = 8^(6-1) = 8^5
Now, calculating 8 to the power of 5, we get:
8 x 8 x 8 x 8 x 8 = 32,768.
So, the answer to 8^6 divided by 8 is 32,768.
Regarding the division of powers of ten, as in the case of (2.4 × 10¹³) divided by (8 × 10⁷), you first simplify the coefficients (2.4 ÷ 8) and then subtract the exponents of the powers of ten (13 - 7 = 6). This process will yield the answer in scientific notation, which is the preferred way to handle very large or very small numbers.