Pertanyaan

Sederhanakanlah bentuk-bentuk pangkat berikut. 10 k − 5 m 8 n 6 ⎝ ⎛ 2 3 k m 6 4 n 3 2 ⎠ ⎞ 3 = ...

Sederhanakanlah bentuk-bentuk pangkat berikut.

$\frac{⎝ ⎛ 2 3 k m ^{\frac{4}{6}} n ^{\frac{2}{3}} ⎠ ⎞ ^{3}}{10 k ^{- 5} m ^{8} n ^{6}} = ...$

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Jawaban terverifikasi

Jawaban

bentuk sederhanya adalah .

bentuk sederhanya adalah $begin mathsize 14px style fraction numerator 4 k to the power of 6 over denominator 5 m to the power of 6 n to the power of 4 end fraction end style$ .

Pembahasan

Gunakan sifat bentuk eksponen berikut: Perhatikan perhitungan berikut: Jadi, bentuk sederhanya adalah .

Gunakan sifat bentuk eksponen berikut:

Perhatikan perhitungan berikut:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row blank blank cell fraction numerator open parentheses 2 cube root of k m to the power of begin display style 4 over 6 end style end exponent n to the power of begin display style 2 over 3 end style end exponent close parentheses cubed over denominator 10 k to the power of negative 5 end exponent m to the power of 8 n to the power of 6 end fraction end cell row blank equals cell fraction numerator open parentheses 2 k to the power of begin display style 1 third end style end exponent m to the power of begin display style 4 over 6 end style end exponent n to the power of begin display style 2 over 3 end style end exponent close parentheses cubed over denominator 10 k to the power of negative 5 end exponent m to the power of 8 n to the power of 6 end fraction end cell row blank equals cell fraction numerator 2 cubed k to the power of begin display style 1 third end style cross times 3 end exponent m to the power of begin display style 4 over 6 cross times 3 end style end exponent n to the power of begin display style 2 over 3 cross times 3 end style end exponent over denominator 10 k to the power of negative 5 end exponent m to the power of 8 n to the power of 6 end fraction end cell row blank equals cell fraction numerator 8 k m squared n squared over denominator 10 k to the power of negative 5 end exponent m to the power of 8 n to the power of 6 end fraction end cell row blank equals cell fraction numerator 4 k to the power of 1 minus open parentheses negative 5 close parentheses end exponent m to the power of 2 minus 8 end exponent n to the power of 2 minus 6 end exponent over denominator 5 end fraction end cell row blank equals cell fraction numerator 4 k to the power of 6 m to the power of negative 6 end exponent n to the power of negative 4 end exponent over denominator 5 end fraction end cell row blank equals cell fraction numerator 4 k to the power of 6 over denominator 5 m to the power of 6 n to the power of 4 end fraction end cell end table end style$

Jadi, bentuk sederhanya adalah $begin mathsize 14px style fraction numerator 4 k to the power of 6 over denominator 5 m to the power of 6 n to the power of 4 end fraction end style$ .