If you try to do this in your calculator, it will explode simply because of how large the number is. This question can be solved - BY HAND - with factors and exponent rules.
The factors of 10 are 2 and 5 and 1 and 10. We use 2 and 5 in this problem as we can write [tex] 10^{999} = (5*2)^{999} = 5^{999} * 2^{999} [/tex]
So, [tex] 10^{999} * 5^{-998} * 2^{-997] [/tex]
[tex] = (5*2)^{999} * 5^{-998} * 2^{-997} [/tex]
[tex] = 5^{999} * 2^{999}* 5^{-998} * 2^{-997} [/tex]
[tex] = 5^{1}2^{2} = 5 * 4 = 20. [/tex]
For the next problem, if we take apart the first part and write it as [tex] 10^{999} = (5*2)^{999} = 5^{999} * 2^{999} [/tex], we have all our exponents adding to zero, and any nonzero power to a zero exponent is 1.
Thus, the two computations are 20 and 1.
