Q. Chii`
[tex] \sf\frac{ {2}^{4} \: \times \: {5}^{ - 3} \: \times \: {9}^{2} }{8 \: \times \: {3}^{6} \: \times \: {125}^{ - 1} } = ....[/tex]
hasilnya adalah...
[tex] \sf\frac{ {2}^{4} \: \times \: {5}^{ - 3} \: \times \: {9}^{2} }{8 \: \times \: {3}^{6} \: \times \: {125}^{ - 1} } = ....[/tex]
hasilnya adalah...
Verified answer
Kelas : IX
Mapel : Matematika
Bab : I - Bilangan Berpangkat
Kode : 9.2.1
[tex] \\ [/tex]
[tex] \dfrac{ 2^4\times 5^{-3}\times 9^2 }{ 8\times 3^6 \times 125^{-1}} [/tex]
Ubah bilangan pokoknya.
[tex] = \dfrac{ 2^4\times 5^{-3}\times (3^2)^2 }{ (2^3)\times 3^6 \times (5^3)^{-1}} [/tex]
Terapkan sifat eksponen [tex] (a^x)^y = a^{xy} [/tex]
[tex] = \dfrac{ 2^4\times 5^{-3}\times 3^4 }{ 2^3\times 3^6 \times 5^{-3}} [/tex]
Terapkan sifat eksponen [tex] \dfrac{ a^x }{ a^y } =a^{x-y} [/tex]
[tex] =2^{(4-3)}\times 5^{(-3-(-3))}\times 3^{(4-6)} [/tex]
Sederhanakan.
[tex] =2^{1}\times 5^{(-3+3)}\times 3^{-2} [/tex]
[tex] =2\times 5^{0}\times 3^{-2} [/tex]
[tex] =2\times 1\times 3^{-2} [/tex]
[tex] =2\times 3^{-2} [/tex]
Terapkan sifat [tex] a^{-x}=\dfrac{ 1 }{ a^x } [/tex]
[tex] =2\times \dfrac{1 }{ 3^2 } [/tex]
[tex] =2\times \dfrac{1 }{ 9 } [/tex]
[tex] =\boxed{ \dfrac{2 }{ 9 } } [/tex]
[tex] \\ [/tex]
#TingkatkanPrestasimu
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2⁴/8 = 16/8 = 2
5⁻³/(125⁻¹) = 5⁻³/(5³⁽⁻¹⁾) = 5⁻³/5⁻³ = 1
9²/3⁶ = (3²)²/(3⁶) = 3⁴/3⁶ = 3⁴⁻⁶ = 3⁻²
Therefore..
2(1)(3⁻²) = 2(1)/(3²) = ²/₉
(xcvi)