Pertanyaan

Jika x = 7 199 ( 2 198 × 1 5 199 + 6 199 × 5 197 ) 2 × 5 197 ( 2 197 × 2 1 200 − 7 200 × 6 198 ) , maka nilai dari x 4 1 adalah ....

Jika $x = \frac{2 \times 5 ^{197} ( 2 ^{197} \times 2 1 ^{200} - 7 ^{200} \times 6 ^{198} )}{7 ^{199} ( 2 ^{198} \times 1 5 ^{199} + 6 ^{199} \times 5 ^{197} )}$ , maka nilai dari $x^{\frac{1}{4}}$ adalah ....

$fraction numerator square root of size 14px 7 over denominator size 14px 3 end fraction$
$fraction numerator size 14px 7 square root of size 14px 3 over denominator size 14px 3 end fraction$

K. Nurul

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Ingat bahwa , , dan . Maka, bentuk pada soal dapat kita sederhanakan menjadi Dengan demikian, kita peroleh Jadi, jawaban yang tepat adalah C.

Ingat bahwa , , dan .

Maka, bentuk pada soal dapat kita sederhanakan menjadi

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row x equals cell fraction numerator 2 cross times 5 to the power of 197 left parenthesis 2 to the power of 197 cross times 21 to the power of 200 minus 7 to the power of 200 cross times 6 to the power of 198 right parenthesis over denominator 7 to the power of 199 left parenthesis 2 to the power of 198 cross times 15 to the power of 199 plus 6 to the power of 199 cross times 5 to the power of 197 right parenthesis end fraction end cell row blank equals cell fraction numerator 2 cross times 5 to the power of 197 left parenthesis 2 to the power of 197 cross times 3 to the power of 200 cross times 7 to the power of 200 minus 7 to the power of 200 cross times 2 to the power of 198 cross times 3 to the power of 198 right parenthesis over denominator 7 to the power of 199 left parenthesis 2 to the power of 198 cross times 3 to the power of 199 cross times 5 to the power of 199 plus 2 to the power of 199 cross times 3 to the power of 199 cross times 5 to the power of 197 right parenthesis end fraction end cell row blank equals cell fraction numerator 2 cross times 5 to the power of 197 cross times 7 to the power of 199 left parenthesis 2 to the power of 197 cross times 3 to the power of 200 cross times 7 minus 7 cross times 2 to the power of 198 cross times 3 to the power of 198 right parenthesis over denominator 2 cross times 5 to the power of 197 cross times 7 to the power of 199 left parenthesis 2 to the power of 197 cross times 3 to the power of 199 cross times 5 squared plus 2 to the power of 198 cross times 3 to the power of 199 right parenthesis end fraction end cell row blank equals cell fraction numerator 2 to the power of 197 cross times 3 to the power of 200 cross times 7 minus 7 cross times 2 to the power of 198 cross times 3 to the power of 198 over denominator 2 to the power of 197 cross times 3 to the power of 199 cross times 5 squared plus 2 to the power of 198 cross times 3 to the power of 199 end fraction end cell row blank equals cell fraction numerator 2 to the power of 197 cross times 3 to the power of 198 left parenthesis 3 squared cross times 7 minus 7 cross times 2 right parenthesis over denominator 2 to the power of 197 cross times 3 to the power of 198 left parenthesis 3 cross times 5 squared plus 2 cross times 3 right parenthesis end fraction end cell row blank equals cell fraction numerator 3 squared cross times 7 minus 7 cross times 2 over denominator 3 cross times 5 squared plus 2 cross times 3 end fraction end cell row blank equals cell fraction numerator 9 cross times 7 minus 7 cross times 2 over denominator 3 cross times 25 plus 2 cross times 3 end fraction end cell row blank equals cell fraction numerator 63 minus 14 over denominator 75 plus 6 end fraction end cell row blank equals cell 49 over 81 end cell end table end style$

Dengan demikian, kita peroleh

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x to the power of 1 fourth end exponent end cell equals cell open parentheses 49 over 81 close parentheses to the power of 1 fourth end exponent end cell row blank equals cell open parentheses 7 squared over 3 to the power of 4 close parentheses to the power of 1 fourth end exponent end cell row blank equals cell 7 to the power of begin display style 2 over 4 end style end exponent over 3 to the power of begin display style 4 over 4 end style end exponent end cell row blank equals cell 7 to the power of begin display style 1 half end style end exponent over 3 end cell row blank equals cell fraction numerator square root of 7 over denominator 3 end fraction end cell end table end style$

Jadi, jawaban yang tepat adalah C.

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