Pertanyaan

Bentuk sederhana dari dengan k merupakan bilangan bulat positif adalah ....

Bentuk sederhana dari $begin mathsize 14px style fraction numerator 5 times 2 to the power of k times open parentheses 5 to the power of 2 k minus 1 end exponent times 2 to the power of k plus 1 end exponent close parentheses cubed over denominator open parentheses 5 to the power of 3 k minus 1 end exponent times 2 to the power of 2 k minus 1 end exponent close parentheses squared end fraction end style$ dengan k merupakan bilangan bulat positif adalah ....

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Klaim

N. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Padang

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$begin mathsize 14px style fraction numerator 5 times 2 to the power of k times open parentheses 5 to the power of 2 k minus 1 end exponent times 2 to the power of k plus 1 end exponent close parentheses cubed over denominator open parentheses 5 to the power of 3 k minus 1 end exponent times 2 to the power of 2 k minus 1 end exponent close parentheses squared end fraction equals fraction numerator 5 times 2 to the power of k times open parentheses 5 to the power of 2 k minus 1 end exponent close parentheses cubed times open parentheses 2 to the power of k plus 1 end exponent close parentheses cubed over denominator open parentheses 5 to the power of 3 k minus 1 end exponent close parentheses squared times open parentheses 2 to the power of 2 k minus 1 end exponent close parentheses squared end fraction equals fraction numerator 5 times 2 to the power of k times 5 to the power of 6 k minus 3 end exponent times 2 to the power of 3 k plus 3 end exponent over denominator 5 to the power of 6 k minus 2 end exponent times 2 to the power of 4 k minus 2 end exponent end fraction equals 5 to the power of 1 plus open parentheses 6 k minus 3 close parentheses minus open parentheses 6 k minus 2 close parentheses end exponent times 2 to the power of k plus open parentheses 3 k plus 3 close parentheses minus open parentheses 4 k minus 2 close parentheses end exponent equals 5 to the power of 0 times 2 to the power of 5 equals 1 times 32 equals box enclose 32 end style$