Pertanyaan

Bentuk sederhana dari 3 − 64 p − 15 r − 9 1296 p 6 q − 10 r 14 adalah ....

Bentuk sederhana dari $\frac{1296 p ^{6} q ^{- 10} r ^{14}}{3 - 64 p ^{- 15} r ^{- 9}}$ adalah ....

$begin mathsize 14px style negative fraction numerator 9 p to the power of 8 r to the power of 7 over denominator q squared end fraction end style$
$begin mathsize 14px style negative fraction numerator 9 p to the power of 8 r to the power of 10 over denominator q to the power of 5 end fraction end style$
$begin mathsize 14px style negative fraction numerator 9 p to the power of 8 r to the power of 7 over denominator 2 q squared end fraction end style$
$begin mathsize 14px style negative fraction numerator 9 p to the power of 10 r to the power of 11 over denominator 2 q to the power of 5 end fraction end style$

K. Nurul

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Perhatikan bahwa Jadi, hasil dari adalah . Dengan demikian, jawaban yang tepat adalah B.

Perhatikan bahwa

$begin mathsize 12px style fraction numerator blank square root of 1296 p to the power of 6 q to the power of negative 10 end exponent r to the power of 14 end root over denominator cube root of negative 64 p to the power of negative 15 end exponent r to the power of negative 9 end exponent end root end fraction equals fraction numerator blank square root of open parentheses 2 to the power of 4 times 3 to the power of 4 close parentheses p to the power of 6 q to the power of negative 10 end exponent r to the power of 14 end root over denominator cube root of open parentheses negative 4 close parentheses cubed p to the power of negative 15 end exponent r to the power of negative 9 end exponent end root end fraction equals fraction numerator blank open parentheses open parentheses 2 to the power of 4 times 3 to the power of 4 close parentheses p to the power of 6 q to the power of negative 10 end exponent r to the power of 14 close parentheses to the power of 1 half end exponent over denominator open parentheses left parenthesis negative 4 right parenthesis cubed p to the power of negative 15 end exponent r to the power of negative 9 end exponent close parentheses to the power of 1 third end exponent end fraction equals fraction numerator blank 2 to the power of 4 cross times 1 half end exponent times 3 to the power of 4 cross times 1 half end exponent times p to the power of 6 cross times 1 half end exponent times q to the power of negative 10 cross times 1 half end exponent times r to the power of 14 cross times 1 half end exponent over denominator open parentheses open parentheses negative 4 close parentheses cubed close parentheses to the power of 1 third end exponent times p to the power of negative 15 cross times 1 third end exponent times r to the power of negative 9 cross times 1 third end exponent end fraction equals fraction numerator blank 2 squared times 3 squared times p cubed times q to the power of negative 5 end exponent times r to the power of 7 over denominator negative 4 times p to the power of negative 5 end exponent times r to the power of negative 3 end exponent end fraction equals fraction numerator blank 2 squared times 3 squared times p cubed times q to the power of negative 5 end exponent times r to the power of 7 over denominator negative 1 times 2 squared times p to the power of negative 5 end exponent times r to the power of negative 3 end exponent end fraction equals fraction numerator 2 to the power of 2 minus 2 end exponent times 3 squared times p to the power of 3 minus stretchy left parenthesis negative 5 stretchy right parenthesis end exponent times q to the power of negative 5 end exponent times r to the power of 7 minus stretchy left parenthesis negative 3 stretchy right parenthesis end exponent over denominator negative 1 end fraction equals negative 2 to the power of 0 times 3 squared times p to the power of 8 times q to the power of negative 5 end exponent times r to the power of 10 equals negative fraction numerator 3 squared times p to the power of 8 times r to the power of 10 over denominator q to the power of 5 end fraction equals negative fraction numerator 9 p to the power of 8 r to the power of 10 over denominator q to the power of 5 end fraction end style$

Jadi, hasil dari $begin mathsize 14px style fraction numerator blank square root of 1296 p to the power of 6 q to the power of negative 10 end exponent r to the power of 14 end root over denominator cube root of negative 64 p to the power of negative 15 end exponent r to the power of negative 9 end exponent end root end fraction end style$ adalah .

Dengan demikian, jawaban yang tepat adalah B.