Pertanyaan

( 81 a 9 ⋅ b − 2 3 a 6 ⋅ b − 5 ) − 1 = ...

$(\frac{3 a ^{6} \cdot b ^{- 5}}{81 a ^{9} \cdot b ^{- 2}})^{- 1} = ...$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Ingat kembali sifat bilangan berpangkat berikut. sehingga diperoleh perhitungan: Dengan demikian, nilai dari adalah . Jadi, jawaban yang tepat adalah C.

Ingat kembali sifat bilangan berpangkat berikut.

open parentheses a to the power of m close parentheses to the power of n equals a to the power of m times n end exponent comma space a not equal to 0

a to the power of n equals stack stack a cross times a cross times a cross times... cross times a with underbrace below with a space s e b a n y a k space n below comma space a not equal to 0

a to the power of n over a to the power of m equals a to the power of n minus m end exponent comma space a not equal to 0

sehingga diperoleh perhitungan:

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 3 a to the power of 6 times b to the power of negative 5 end exponent over denominator 81 a to the power of 9 times b to the power of negative 2 end exponent end fraction close parentheses to the power of negative 1 end exponent end cell equals cell open parentheses fraction numerator 3 a to the power of 6 times b to the power of negative 5 end exponent over denominator open parentheses 3 times 3 times 3 times 3 close parentheses a to the power of 9 times b to the power of negative 2 end exponent end fraction close parentheses to the power of negative 1 end exponent end cell row blank equals cell open parentheses fraction numerator 3 a to the power of 6 times b to the power of negative 5 end exponent over denominator 3 to the power of 4 a to the power of 9 times b to the power of negative 2 end exponent end fraction close parentheses to the power of negative 1 end exponent end cell row blank equals cell open parentheses 3 to the power of 1 minus 4 end exponent a to the power of 6 minus 9 end exponent times b to the power of negative 5 minus open parentheses negative 2 close parentheses end exponent close parentheses to the power of negative 1 end exponent end cell row blank equals cell open parentheses 3 to the power of negative 3 end exponent a to the power of negative 3 end exponent times b to the power of negative 3 end exponent close parentheses to the power of negative 1 end exponent end cell row blank equals cell 3 to the power of open parentheses negative 3 close parentheses times open parentheses negative 1 close parentheses end exponent a to the power of open parentheses negative 3 close parentheses end exponent times b to the power of open parentheses negative 3 close parentheses times open parentheses negative 1 close parentheses end exponent end cell row blank equals cell 3 cubed a cubed times b cubed end cell row blank equals cell open parentheses 3 a b close parentheses cubed end cell end table$

Dengan demikian, nilai dari $open parentheses fraction numerator 3 a to the power of 6 times b to the power of negative 5 end exponent over denominator 81 a to the power of 9 times b to the power of negative 2 end exponent end fraction close parentheses to the power of negative 1 end exponent$ adalah open parentheses 3 a b close parentheses cubed .

Jadi, jawaban yang tepat adalah C.