Answer:
[tex]2^{128}[/tex]
Step-by-step explanation:
Using the properties of exponents
• [tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
• [tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{(m-n)}[/tex]
given
[tex](32^4)^{7}[/tex] ÷ 16³
express 32 as [tex]2^{5}[/tex] and 16 as [tex]2^{4}[/tex]
= ( [tex](2^5^{(4)})^7[/tex] ÷ ([tex]2^{4}[/tex] )³
= [tex](2^{20}) ^{7}[/tex] ÷ [tex]2^{12}[/tex]
= [tex]2^{140}[/tex] ÷ [tex]2^{12}[/tex]
= [tex]2^{(140-12)}[/tex]
= [tex]2^{128}[/tex]
