= 16/(aⁿ⁺²)
pembahasan :
lihat lampiran.
aⁿ × aᵐ = aⁿ ⁺ ᵐ
aⁿ / aᵐ = aⁿ ⁻ ᵐ
( aⁿ ) ᵐ = aⁿ ˣ ᵐ
Sifat Eksponen
[tex]a^{m} \times a^{n} = a^{m+n}\\[/tex]
[tex]\frac{a^{m}}{a^{n}} = a^{m-n}\\[/tex]
[tex](a^{m})^{n} = a^{m \times n}\\[/tex]
[tex]a^{m} . b^{m} = (a . b)^{m}\\[/tex]
[tex]\frac{1}{a^{m}} = a^{-m}\\[/tex]
[tex]\\[/tex]
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[tex] \frac{ {(2. {a}^{n} })^{3} . {a}^{3} }{ \frac{1}{2}. {a}^{3n + 3} } \div \frac{( {a}^{n + 1} )^{3} }{a. {a}^{2n} } \\ = \frac{ { {2}^{3}. {a}^{3n} } . {a}^{3} }{ {2}^{ - 1} . {a}^{3n + 3} } \div \frac{{a}^{3(n + 1)} }{ {a}^{1 + 2n} } \\ = \frac{ { {2}^{3}. {a}^{3n} } . {a}^{3} }{ {2}^{ - 1} . {a}^{3n + 3} } \div \frac{{a}^{3n + 3} }{ {a}^{1 + 2n} } \\ = \frac{ { {2}^{3} {a}^{3n + 3} } }{ {2}^{ - 1} .{a}^{3n + 3} } \times \frac{ {a}^{1 + 2n} } {{a}^{3n + 3} } \\ = \frac{ { {2}^{3} } }{ {2}^{ - 1} . {a}^{3n + 3} } \times {a}^{1 + 2n} \\ = \frac{ { {2}^{3} . {a}^{1 + 2n} } }{ {2}^{ - 1} .{a}^{3n + 3} } \\ = {2}^{3 - ( - 1)} . \: {a}^{(1 + 2n) - (3n + 3)} \\ = {2}^{3 + 1} . \: {a}^{1 + 2n - 3n - 3} \\ = {2}^{4} . {a}^{ - n - 2} \\ = 16 \: . \: {a}^{ - (n + 2)} \\ = \frac{16}{ {a}^{n + 2} } [/tex]
Semoga membantu.
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