Pertanyaan

Nilai dari 6 ( 8 ) 3 2 × 3 ( 125 ) 2 − 1 adalah ....

Nilai dari $6 (8)^{\frac{2}{3}} \times 3 (125)^{\frac{- 1}{2}}$ adalah ....

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai dari adalah .

nilai dari $6 open parentheses 8 close parentheses to the power of 2 over 3 end exponent cross times 3 open parentheses 125 close parentheses to the power of fraction numerator negative 1 over denominator 2 end fraction end exponent$ adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 72 over 25 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 5 end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 72 over 25 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 5 end cell end table

Pembahasan

Ingat kembali aturan bilangan berpangkat berikut ini! Dengan aturandi atas, didapat perhitungan berikut ini. Dengan demikian, nilai dari adalah .

Ingat kembali aturan bilangan berpangkat berikut ini!

a to the power of m over n end exponent equals n-th root of a to the power of m end root a to the power of negative n end exponent equals 1 over a to the power of n

Dengan aturan di atas, didapat perhitungan berikut ini.

$table attributes columnalign right center left columnspacing 0px end attributes row cell 6 open parentheses 8 close parentheses to the power of 2 over 3 end exponent cross times 3 open parentheses 125 close parentheses to the power of fraction numerator negative 1 over denominator 2 end fraction end exponent end cell equals cell 6 cube root of 8 squared end root cross times 3 square root of 125 to the power of negative 1 end exponent end root end cell row blank equals cell 6 open parentheses cube root of 64 close parentheses cross times 3 open parentheses square root of 1 over 125 end root close parentheses end cell row blank equals cell 6 open parentheses 4 close parentheses cross times fraction numerator 3 over denominator square root of 25 cross times 5 end root end fraction end cell row blank equals cell fraction numerator 72 over denominator 5 square root of 5 end fraction end cell row blank equals cell fraction numerator 72 over denominator 5 square root of 5 end fraction cross times fraction numerator square root of 5 over denominator square root of 5 end fraction end cell row blank equals cell 72 over 25 square root of 5 end cell end table$

Dengan demikian, nilai dari $6 open parentheses 8 close parentheses to the power of 2 over 3 end exponent cross times 3 open parentheses 125 close parentheses to the power of fraction numerator negative 1 over denominator 2 end fraction end exponent$ adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 72 over 25 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 5 end cell end table .