Respuesta :

sqdancefan

Answer:

[tex]1024^{10}\\b^{1+m}\\16^{25}[/tex]

Step-by-step explanation:

1.

[tex]2^{100}=\left(2^{10}\right)^{10}=1024^{10}[/tex]

2.

[tex]b\cdot b^{m}=b^{1}\cdot b^{m}=b^{1+m}[/tex]

3.

[tex]2^{100}=\left(2^{4}\right)^{25}=16^{25}[/tex]

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The applicable rules of exponents are ...

[tex]\left(a^{b}\right)^{c}=a^{b\cdot c}\\\\a^{b}\cdot a^{c}=a^{b+c}[/tex]

note that [tex]2^{10}[/tex] = 1024, hence

[tex]2^{100}[/tex] = (2^10)^10 = [tex]1024^{10}[/tex]

note that [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{m+n}[/tex], thus

b × [tex]b^{m}[/tex] = [tex]b^{1+m}[/tex]

note that [tex]2^{4}[/tex] = 16, hence

[tex]2^{100}[/tex] =  ([tex]2^{4}[/tex])^25 = [tex]16^{25}[/tex]