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Bentuk sederhana dari ((2a)3b2)−2(a2b−2)5​ adalah ....

Pertanyaan

Bentuk sederhana dari open parentheses a squared b to the power of negative 2 end exponent close parentheses to the power of 5 over open parentheses open parentheses 2 a close parentheses cubed b squared close parentheses to the power of negative 2 end exponent adalah ....

  1. fraction numerator 64 a to the power of 16 over denominator b to the power of 6 end fraction 

  2. fraction numerator a to the power of 7 over denominator 8 b to the power of 24 end fraction

  3. fraction numerator a to the power of 10 over denominator 64 b to the power of 14 end fraction

  4. fraction numerator 64 a b to the power of 10 over denominator b to the power of negative 6 end exponent end fraction

Pembahasan:

Ingat kembali konsep bilangan berpangkat.

table attributes columnalign right center left columnspacing 2px 2px 2px end attributes row cell open parentheses a to the power of b close parentheses to the power of c end cell equals cell a to the power of b cross times c end exponent end cell row cell open parentheses a cross times b close parentheses to the power of m end cell equals cell a to the power of m cross times b to the power of m end cell row cell a to the power of m over a to the power of n end cell equals cell a to the power of m minus n end exponent end cell row cell a to the power of negative n end exponent end cell equals cell 1 over a to the power of n end cell end table

Akan ditentukan bentuk sederhana dari open parentheses a squared b to the power of negative 2 end exponent close parentheses to the power of 5 over open parentheses open parentheses 2 a close parentheses cubed b squared close parentheses to the power of negative 2 end exponent.

table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses a squared b to the power of negative 2 end exponent close parentheses to the power of 5 over open parentheses open parentheses 2 a close parentheses cubed b squared close parentheses to the power of negative 2 end exponent end cell equals cell fraction numerator open parentheses a squared close parentheses to the power of 5 open parentheses b to the power of negative 2 end exponent close parentheses to the power of 5 over denominator open parentheses 8 a cubed b squared close parentheses to the power of negative 2 end exponent end fraction end cell row blank equals cell fraction numerator a to the power of 2 cross times 5 end exponent b to the power of negative 2 cross times 5 end exponent over denominator open parentheses 8 a cubed close parentheses to the power of negative 2 end exponent open parentheses b squared close parentheses to the power of negative 2 end exponent end fraction end cell row blank equals cell fraction numerator a to the power of 10 b to the power of negative 10 end exponent over denominator 8 to the power of negative 2 end exponent a to the power of 3 cross times open parentheses negative 2 close parentheses end exponent b to the power of 2 cross times open parentheses negative 2 close parentheses end exponent end fraction end cell row blank equals cell fraction numerator 8 squared a to the power of 10 b to the power of negative 10 end exponent over denominator a to the power of negative 6 end exponent b to the power of negative 4 end exponent end fraction end cell row blank equals cell 64 times a to the power of 10 over a to the power of negative 6 end exponent times b to the power of negative 10 end exponent over b to the power of negative 4 end exponent end cell row blank equals cell 64 a to the power of 10 minus open parentheses negative 6 close parentheses end exponent b to the power of negative 10 minus open parentheses negative 4 close parentheses end exponent end cell row blank equals cell 64 a to the power of 10 plus 6 end exponent b to the power of negative 10 plus 4 end exponent end cell row blank equals cell 64 a to the power of 16 b to the power of negative 6 end exponent end cell row blank equals cell fraction numerator 64 a to the power of 16 over denominator b to the power of 6 end fraction end cell end table

Diperoleh open parentheses a squared b to the power of negative 2 end exponent close parentheses to the power of 5 over open parentheses open parentheses 2 a close parentheses cubed b squared close parentheses to the power of negative 2 end exponent equals fraction numerator 64 a to the power of 16 over denominator b to the power of 6 end fraction.

Jadi, jawaban yang tepat adalah A.

Jawaban terverifikasi

Dijawab oleh:

Y. Fathoni

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

Terakhir diupdate 07 Oktober 2021

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