Question

Need help! multiple questions [LOTS OF POINTS] Please help! show work thanks

Answer 1

Answer:

$1024^{10}\\b^{1+m}\\16^{25}$

Step-by-step 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 ...

$\left(a^{b}\right)^{c}=a^{b\cdot c}\\\\a^{b}\cdot a^{c}=a^{b+c}$

Answer 2

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 = $16^{25}$