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Simplify [tex](32^4)^7 / 16^3[/tex], leaving answer as index notation

Simplify Tex3247 163tex Leaving Answer As Index Notation class=

Sagot :

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]

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