If n is a positive integer and X 2n = 2, try to find the value of (- 3x3n) 2-4 (- x2) 2n

If n is a positive integer and X 2n = 2, try to find the value of (- 3x3n) 2-4 (- x2) 2n

The original formula = 9x6n-4x4n = 9 (X2N) 3-4 (X2N) 2,
When X2N = 2, the original formula = 9 × 23-16 = 56

Guess: the 2n power of a under the root sign = (), and the 3N power of a under the third root sign = ()

The 2n power of a under the root sign = (the nth power of a), and the 3N power of a under the cubic root sign = (the nth power of a)

Lim radical n ^ 2 + N + 1 / 3n-2

lim【n→∞】√(n²+n+1)/(3n-2)
=lim【n→∞】√(1+1/n+1/n²)/(3-2/n²)
=√(1+0+0)/(3-0)
=1/3
Answer: 1 / 3

Given a ^ 2n = (2 under the radical) + 1, find the value of (a ^ 3N + A ^ - 3n) / (a ^ n + A ^ - n)

(a^3n+a^-3n)/(a^n+a^-n)=[(a^3n+a^-3n)/a^n]/[(a^n+a^-n)/a^n]
=(a^2n+a^-4n)/(1+a^-2n)
={(2 under the root) + 1 + [(2 under the root) + 1] ^ - 2} / {1 + [(2 under the root) + 1] ^ - 1}
=2 times (2 under root) - 1

The 3n-1 power of B is divided by the 2n + 1 power of a, and then divided by the 3n-2 power of B divided by the 2n power of A B ^ (3n-1) C on the molecule / A ^ (2n + 1) on the denominator △ B ^ (3n-2) on the molecule / A ^ 2n on the denominator

Original formula = B / A

The 3N power of 16 is divided by the 2n power of 8 and removed to the 1st power of 4

(2^4)^3n/(2^3)^2n/2^2=2^(12n-6n-2)=2^(6n-2)

If the 2n power of a = 3, find the value of the fourth power of (a to the 3N power)

(a to the power of 3n)
=The 3N × 4 power of a
=The 2n × 6th power of a
=(a to the power of 2n)
=The sixth power of 3
=729

81's nth power multiplied by 8's 2n + 1 power divided by 12's 3N power divided by 3's nth power

81^N*8^(2N+1)/(12^(3N)*3^N)
=3^(4N)*2^(6N+3)/[3^(3N)*2^(6N)*3^N]
=3^[4N-3N-N]*2^[(6N+3)-6N]
=3^0*2^3
=1*8
=8

Let n be a positive integer and X 2n = 4. Find the value of 9 (x 3n) 2-13 (x 2) 2n

∵x2n=4，
∴9（x3n）2-13（x2）2n，
=9（x2n）3-13（x2n）2，
=9×43-13×42，
=368．
So the answer is: 368

Given that n is a positive integer, and the 2nd power of (x to the nth power) is 9, find the 2nd power of (3N power of x) - 2n power of 3 (square of x)

(x^n)^2=9
x^(2n)=9
So:
(x^3n)^2-3(x^2)^2n
=(x^2n)^3-3(x^2n)^2
=9^3-3*9^2=486