Pertanyaan

Sederhanakan operasi bilangan berpangkat berikut ! a. a − 2 1 × a − 6 5 × a − 3 1 b. x 3 × x 8 3 × x − 4 1 × x − 4 3

Sederhanakan operasi bilangan berpangkat berikut !

a. $a^{- \frac{1}{2}} \times a^{- \frac{5}{6}} \times a^{- \frac{1}{3}}$
b. $x^{3} \times x^{\frac{3}{8}} \times x^{- \frac{1}{4}} \times x^{- \frac{3}{4}}$

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E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

bentuk sederhana dari , dan .

bentuk sederhana dari $a to the power of negative 1 half end exponent cross times a to the power of negative 5 over 6 end exponent cross times a to the power of negative 1 third end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator a space cube root of a squared end root end fraction end cell end table$ , dan x cubed space cross times space x to the power of 3 over 8 end exponent space cross times space x to the power of negative 1 fourth end exponent space cross times space x to the power of negative 3 over 4 end exponent equals x squared space root index 8 of x cubed end root

x cubed space cross times space x to the power of 3 over 8 end exponent space cross times space x to the power of negative 1 fourth end exponent space cross times space x to the power of negative 3 over 4 end exponent equals x squared space root index 8 of x cubed end root

Pembahasan

Ingatlah sifat-sifat bilangan berpangkat berikut. Berdasarkan sifat-sifat di atas, maka: a) b) Dengan demikian, bentuk sederhana dari , dan .

Ingatlah sifat-sifat bilangan berpangkat berikut.

Berdasarkan sifat-sifat di atas, maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell a to the power of negative 1 half end exponent cross times a to the power of negative 5 over 6 end exponent cross times a to the power of negative 1 third end exponent end cell equals cell a to the power of negative 1 half plus open parentheses negative 5 over 6 close parentheses plus open parentheses negative 1 third close parentheses end exponent end cell row blank equals cell a to the power of fraction numerator negative 3 minus 5 minus 2 over denominator 6 end fraction end exponent end cell row blank equals cell a to the power of negative 10 over 6 end exponent end cell row blank equals cell a to the power of negative 5 over 3 end exponent end cell row blank equals cell 1 over a to the power of begin display style 5 over 3 end style end exponent end cell row blank equals cell fraction numerator 1 over denominator cube root of a to the power of 5 end root end fraction end cell row blank equals cell fraction numerator 1 over denominator cube root of a cubed times a squared end root end fraction end cell row blank equals cell fraction numerator 1 over denominator a space cube root of a squared end root end fraction end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell x cubed space cross times space x to the power of 3 over 8 end exponent space cross times space x to the power of negative 1 fourth end exponent space cross times space x to the power of negative 3 over 4 end exponent end cell equals cell x to the power of 3 plus 3 over 8 plus open parentheses negative 1 fourth close parentheses plus open parentheses negative 3 over 4 close parentheses end exponent end cell row blank equals cell x to the power of fraction numerator 24 plus 3 minus 2 minus 6 over denominator 8 end fraction end exponent end cell row blank equals cell x to the power of 19 over 8 end exponent end cell row blank equals cell root index 8 of x to the power of 19 end root end cell row blank equals cell root index 8 of x to the power of 16 times x cubed end root end cell row blank equals cell x squared space root index 8 of x cubed end root end cell end table$

Dengan demikian, bentuk sederhana dari $a to the power of negative 1 half end exponent cross times a to the power of negative 5 over 6 end exponent cross times a to the power of negative 1 third end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator a space cube root of a squared end root end fraction end cell end table$ , dan x cubed space cross times space x to the power of 3 over 8 end exponent space cross times space x to the power of negative 1 fourth end exponent space cross times space x to the power of negative 3 over 4 end exponent equals x squared space root index 8 of x cubed end root .