Question

Need help! multiple questions [LOTS OF POINTS]

Please help! show work

thanks

Answer 1

note that
`2^(10)` = 1024, hence

`2^(100)` = (2^10)^10 =
`1024^(10)`

note that
`a^(m)` ×
`a^(n)` =
`a^(m+n)`, thus

b ×
`b^(m)` =
`b^(1+m)`

note that
`2^(4)` = 16, hence

`2^(100)` = (
`2^(4)`)^25 =
`16^(25)`

Answer 2

`1024^(10)\\b^(1+m)\\16^(25)`

Explanation:

1.

`2^(100)=\left(2^(10)\right)^(10)=1024^(10)`

2.

`b\cdot b^(m)=b^(1)\cdot b^(m)=b^(1+m)`

3.

`2^(100)=\left(2^(4)\right)^(25)=16^(25)`

_____

The applicable rules of exponents are ...

`\left(a^(b)\right)^(c)=a^(b\cdot c)\\\\a^(b)\cdot a^(c)=a^(b+c)`