Tentukan hasil pemangkatan bilangan berpangkat berikut ! a. 892×894 b. 421×4−1 c. 943×986

Pertanyaan

Tentukan hasil pemangkatan bilangan berpangkat berikut !

a. $8^\frac29\times8^\frac49$
b. $4^\frac12\times4^{-1}$
c. $9^\frac34\times9^\frac68$

D. Nuryani

Master Teacher

Mahasiswa/Alumni Universitas Padjadjaran

Jawaban terverifikasi

Jawaban

hasil dari 8 to the power of 2 over 9 end exponent cross times 8 to the power of 4 over 9 end exponent equals 4

4 to the power of 1 half end exponent cross times 4 to the power of negative 1 end exponent equals 1 half

, dan

9 to the power of 3 over 4 end exponent cross times 9 to the power of 6 over 8 end exponent equals 27

Pembahasan

Ingatlah sifat-sifat bilangan berpangkat berikut.

Berdasarkan sifat-sifat di atas, maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell 4 to the power of 1 half end exponent cross times 4 to the power of negative 1 end exponent end cell equals cell 4 to the power of 1 half plus open parentheses negative 1 close parentheses end exponent end cell row blank equals cell 4 to the power of 1 half minus 1 end exponent end cell row blank equals cell 4 to the power of fraction numerator 1 minus 2 over denominator 2 end fraction end exponent end cell row blank equals cell 4 to the power of negative 1 half end exponent end cell row blank equals cell 1 over 4 to the power of begin display style 1 half end style end exponent end cell row blank equals cell fraction numerator 1 over denominator square root of 4 end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 2 squared end root end fraction end cell row blank equals cell 1 half end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell 9 to the power of 3 over 4 end exponent cross times 9 to the power of 6 over 8 end exponent end cell equals cell 9 to the power of 3 over 4 plus 6 over 8 end exponent end cell row blank equals cell 9 to the power of fraction numerator 6 plus 6 over denominator 8 end fraction end exponent end cell row blank equals cell 9 to the power of 12 over 8 end exponent end cell row blank equals cell 9 to the power of 3 over 2 end exponent end cell row blank equals cell square root of 9 cubed end root end cell row blank equals cell square root of 729 end cell row blank equals 27 end table$

Dengan demikian, hasil dari 8 to the power of 2 over 9 end exponent cross times 8 to the power of 4 over 9 end exponent equals 4 , 4 to the power of 1 half end exponent cross times 4 to the power of negative 1 end exponent equals 1 half , dan 9 to the power of 3 over 4 end exponent cross times 9 to the power of 6 over 8 end exponent equals 27 .