Question

0.25的23次方×4的24次方减8的42次方×0.5的128次方是什么

0.25的23次方×4的24次方减8的42次方×0.5的128次方是什么

Answer 1

解：原式=0.25^23×4^24-8^42×0.5^128

=0.25^23x2^48-2^(3x42)x(0.25x2)^128
=0.25^23x2^48-2^126x0.25^128x2^128
=2^48(0.25^23-2^206x0.25^128)
=2^48x0.25^23(1-2^106x0.25^105)
=2^23x2^25x0.25^23(1-2x(2x0.25)^105)
=(2x0.25)^23x2^25(1-2x0.5^105)
=0.5^23x2^25(1-2^(-104))
=2^2(1-2^(-104))
=4-2^(-102)

Answer 2

0.25的23次方×4的24次方 - 8的42次方×0.5的128次方
= 0.25的23次方×4的23次方×4 - 2³的42次方×0.5的128次方
= （0.25×4）的23次方×4 - 2的126次方×0.5的126次方×0.5²

= 1×4 - (2×0.5)的126次方×0.5²
= 4 - 1×0.25
= 4-0.25
= 3.75