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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 to the power of 2 over 9 end exponent cross times 8 to the power of 4 over 9 end exponent
b. 4 to the power of 1 half end exponent cross times 4 to the power of negative 1 end exponent
c. 9 to the power of 3 over 4 end exponent cross times 9 to the power of 6 over 8 end exponent

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.

left parenthesis straight i right parenthesis space a to the power of m over n end exponent equals n-th root of a to the power of m end root left parenthesis ii right parenthesis space a to the power of m cross times a to the power of n equals a to the power of m plus n end exponent left parenthesis iii right parenthesis space a to the power of negative m end exponent equals 1 over a to the power of m    

Berdasarkan sifat-sifat di atas, maka:

a)

table attributes columnalign right center left columnspacing 0px end attributes row cell 8 to the power of 2 over 9 end exponent cross times 8 to the power of 4 over 9 end exponent end cell equals cell 8 to the power of 2 over 9 plus 4 over 9 end exponent end cell row blank equals cell 8 to the power of 6 over 9 end exponent end cell row blank equals cell 8 to the power of 2 over 3 end exponent end cell row blank equals cell cube root of 8 squared end root end cell row blank equals cell cube root of 64 end cell row blank equals cell cube root of 4 cubed end root end cell row blank equals 4 end table

b)

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

c)

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.

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