Question

Compute 10^999* 5^-998* 2^-997. and Compute 10^999* 5^-999* 2^-999

thx in advance

Answer 1

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
`10^(999) = (5*2)^(999) = 5^(999) * 2^(999)`

So,
`10^(999) * 5^(-998) * 2^{-997]`

`= (5*2)^(999) * 5^(-998) * 2^(-997)`

`= 5^(999) * 2^(999)* 5^(-998) * 2^(-997)`

`= 5^(1)2^(2) = 5 * 4 = 20.`

For the next problem, if we take apart the first part and write it as
`10^(999) = (5*2)^(999) = 5^(999) * 2^(999)`, 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.