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Tentukan hasil pemangkatan bilangan berpangkat berikut ! d. 16−21​×1641​ e. 3257​÷3253​ f. 49−61​÷4931​

Pertanyaan

Tentukan hasil pemangkatan bilangan berpangkat berikut !

d. 16 to the power of negative 1 half end exponent cross times 16 to the power of 1 fourth end exponent
e. 32 to the power of 7 over 5 end exponent divided by 32 to the power of 3 over 5 end exponent
f. 49 to the power of negative 1 over 6 end exponent divided by 49 to the power of 1 third end exponent

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 m divided by a to the power of n equals a to the power of m minus n end exponent left parenthesis iv right parenthesis space open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent left parenthesis straight v 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:

d)

table attributes columnalign right center left columnspacing 0px end attributes row cell 16 to the power of negative 1 half end exponent cross times 16 to the power of 1 fourth end exponent end cell equals cell 16 to the power of negative 1 half plus 1 fourth end exponent end cell row blank equals cell 16 to the power of fraction numerator negative 2 plus 1 over denominator 4 end fraction end exponent end cell row blank equals cell 16 to the power of negative 1 fourth end exponent end cell row blank equals cell 1 over 16 to the power of begin display style 1 fourth end style end exponent end cell row blank equals cell fraction numerator 1 over denominator fourth root of 16 end fraction end cell row blank equals cell fraction numerator 1 over denominator fourth root of 2 to the power of 4 end root end fraction end cell row blank equals cell 1 half end cell end table

e)

table attributes columnalign right center left columnspacing 0px end attributes row cell 32 to the power of 7 over 5 end exponent divided by 32 to the power of 3 over 5 end exponent end cell equals cell 32 to the power of 7 over 5 minus 3 over 5 end exponent end cell row blank equals cell 32 to the power of 4 over 5 end exponent end cell row blank equals cell fifth root of 32 to the power of 4 end root end cell row blank equals cell fifth root of open parentheses 2 to the power of 5 close parentheses to the power of 4 end root end cell row blank equals cell fifth root of 2 to the power of 5 cross times 4 end exponent end root end cell row blank equals cell fifth root of 2 to the power of 20 end root end cell row blank equals cell 2 to the power of 20 over 5 end exponent end cell row blank equals cell 2 to the power of 4 end cell row blank equals 16 end table

f)

table attributes columnalign right center left columnspacing 0px end attributes row cell 49 to the power of negative 1 over 6 end exponent divided by 49 to the power of 1 third end exponent end cell equals cell 49 to the power of negative 1 over 6 minus 1 third end exponent end cell row blank equals cell 49 to the power of fraction numerator negative 1 minus 2 over denominator 6 end fraction end exponent end cell row blank equals cell 49 to the power of negative 3 over 6 end exponent end cell row blank equals cell 49 to the power of negative 1 half end exponent end cell row blank equals cell 1 over 49 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 49 end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 7 squared end root end fraction end cell row blank equals cell 1 over 7 end cell end table

Dengan demikian, hasil dari  16 to the power of negative 1 half end exponent cross times 16 to the power of 1 fourth end exponent equals 1 half, 32 to the power of 7 over 5 end exponent divided by 32 to the power of 3 over 5 end exponent equals 16, dan 49 to the power of negative 1 over 6 end exponent divided by 49 to the power of 1 third end exponent equals 1 over 7.

Jawaban terverifikasi

Dijawab oleh:

D. Nuryani

Mahasiswa/Alumni Universitas Padjadjaran

Terakhir diupdate 07 Oktober 2021

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