Home » simplify (frac{6^{2n + 1} times 9^n times 4^{2n}}{18^n times 2^n times 12^{2n}})

simplify (frac{6^{2n + 1} times 9^n times 4^{2n}}{18^n times 2^n times 12^{2n}})

simplify (frac{6^{2n + 1} times 9^n times 4^{2n}}{18^n times 2^n times 12^{2n}})
  • A.
    32n
  • B.
    3 x 23n – 1
  • C.
    2n
  • D.
    6
  • E.
    1
Correct Answer: Option D
Explanation

(frac{6^{2n + 1} times 9^n times 4^{2n}}{18^n times 2^n times 12^{2n}}) = (frac{(2 times 3^{2n + 1} times 3^{2n}) times 2^{4n}}{(2 times 9)^n times 2^n times (6 times 2^{2n})})
= (frac{(2^{2n + 1} times 3^{2n + 1}) times 3^{2n} times 2^{4n}}{2^n times 3^{2n} times 2^n times 2^{4n} times 3^{2n}})
= (frac{2^{2n} + 1 + 4^n times 3^{2n} + 1 + 2^n}{2^{n + n + 4n} times 3^{2n + 4n} times 3^{2n + 2n}})
= (frac{2^{6n + 1} times 3^{4n + 1}}{2^{6n} x 3^{4n}})
= 26n + 1 – 6n x 34n + 1 – 4n
2 x 3 = 6