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Bentuk sederhana dari  adalah ....

Pertanyaan

Bentuk sederhana dari begin mathsize 14px style fraction numerator 2 to the power of begin display style 5 over 12 end style end exponent times 12 to the power of begin display style 5 over 6 end style end exponent over denominator 8 to the power of begin display style 3 over 4 end style end exponent times 6 to the power of begin display style 1 third end style end exponent end fraction end style adalah .... begin mathsize 14px style space space space space end style 

Pembahasan Soal:

Gunakan sifat bilangan berpangkat berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell a to the power of m times a to the power of n end cell equals cell a to the power of m plus n end exponent 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 open parentheses a b close parentheses to the power of m end cell equals cell a to the power of m times b to the power of m end cell end table end style 

Sehingga bentuk sederhana dari bentuk bilangan berpangkat di atas, diperoleh sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell fraction numerator 2 to the power of begin display style 5 over 12 end style end exponent times 12 to the power of begin display style 5 over 6 end style end exponent over denominator 8 to the power of begin display style 3 over 4 end style end exponent times 6 to the power of begin display style 1 third end style end exponent end fraction end cell equals cell fraction numerator 2 to the power of begin display style 5 over 12 end style end exponent times open parentheses 2 squared times 3 close parentheses to the power of begin display style 5 over 6 end style end exponent over denominator open parentheses 2 cubed close parentheses to the power of begin display style 3 over 4 end style end exponent times open parentheses 2 times 3 close parentheses to the power of begin display style 1 third end style end exponent end fraction end cell row blank equals cell fraction numerator 2 to the power of 5 over 12 end exponent times 2 to the power of 2 cross times 5 over 6 end exponent times 3 to the power of 5 over 6 end exponent over denominator 2 to the power of 3 cross times 3 over 4 end exponent times 2 to the power of 1 third end exponent times 3 to the power of 1 third end exponent end fraction end cell row blank equals cell fraction numerator 2 to the power of 5 over 12 end exponent times 2 to the power of 10 over 6 end exponent times 3 to the power of 5 over 6 end exponent over denominator 2 to the power of 9 over 4 end exponent times 2 to the power of 1 third end exponent times 3 to the power of 1 third end exponent end fraction end cell row blank equals cell 2 to the power of 5 over 12 plus 10 over 6 minus 9 over 4 minus 1 third end exponent times 3 to the power of 5 over 6 minus 1 third end exponent end cell row blank equals cell 2 to the power of fraction numerator 5 plus 20 minus 27 minus 4 over denominator 12 end fraction end exponent times 3 to the power of fraction numerator 5 minus 2 over denominator 6 end fraction end exponent end cell row blank equals cell 2 to the power of negative 6 over 12 end exponent times 3 to the power of 3 over 6 end exponent end cell row blank equals cell 2 to the power of negative 1 half end exponent times 3 to the power of 1 half end exponent end cell row blank equals cell 3 to the power of begin display style 1 half end style end exponent over 2 to the power of 1 half end exponent end cell row blank equals cell fraction numerator square root of 3 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row blank equals cell fraction numerator square root of 6 over denominator 2 end fraction end cell row cell fraction numerator 2 to the power of begin display style 5 over 12 end style end exponent times 12 to the power of begin display style 5 over 6 end style end exponent over denominator 8 to the power of begin display style 3 over 4 end style end exponent times 6 to the power of begin display style 1 third end style end exponent end fraction end cell equals cell 1 half square root of 6 end cell end table end style 

Jadi, bentuk sederhana dari begin mathsize 14px style fraction numerator 2 to the power of begin display style 5 over 12 end style end exponent times 12 to the power of begin display style 5 over 6 end style end exponent over denominator 8 to the power of begin display style 3 over 4 end style end exponent times 6 to the power of begin display style 1 third end style end exponent end fraction end style adalah begin mathsize 14px style 1 half square root of 6 end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 13 Maret 2021

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