It is known that monomials only contain the letter X, and their exponents are 3 and 2 respectively. When x = 2 and y = 3, their values are 24, write this algebraic formula

It is known that monomials only contain the letter X, and their exponents are 3 and 2 respectively. When x = 2 and y = 3, their values are 24, write this algebraic formula

Let this monomial be ax & # 179; Y & # 178; from the meaning of the title
a* 2³ *3²=24,
The solution is a = 1 / 3,
The original monomial formula is 1 / 3 * X & # 179; Y & # 178;
(the original condition "only contains the letter X" is obviously wrong, it should be "only contains X and Y")

The sum of the coefficients is 0, and the value of this algebraic expression is obtained when x is equal to minus one

For example: 2x & # 179; - X-1
When x = - 1,
2x³-x-1
=2×(-1)³-（-1）-1
=-2+1-1
=-2

Algebraic expression: a number 1 larger than the reciprocal of a (a is not 0)

1/a + 1 (a≠0)

Given that M + M 1 / 2 = 1, find the value of M (M + 3) + (1 + 2m) (1-2m)

M + 1 / M = 1 leads to m ^ 2-m + 1 = 0
m(m+3)+(1+2m)(1-2m)=m^2+3m+1-4m^2=-3m^2+3m+1=-3(m^2-m+1)+4=4

Given a ^ m = 2, a ^ n = 4, a ^ k = 6, try to find the value of a ^ 4m-3n + 2K

a^(4m-3n+2k)
=a^(4m+2k)/a^3n
=(a^m)^4*(a^k)^2/(a^n)^3
=2^4*6^2/4^3
=9

If M = 5, n = 2 is a solution of the equation 2m-3n = 2K, then the value of K is?

The solution is k = 2

If (a ^ m × B ^ n × b) ^ 3 = a ^ 9 × B ^ 15, find the value of 2 ^ m + n

(a^m×b^n×b)^3=a^9×b^15
a^3m×b^3(n+1)=a^9×b^15
3m=9 3(n+1)=15
m=3 n=4
2^m+n
=2^(3+4)
=2^7
=128

If (a ^ n * B ^ m * b) ^ 3 = a ^ 9 * B ^ 15, find the value of M, n
^It's a power, and * is a power sign

(a^n*b^m*b)^3
=A ^ (3n) B ^ (3m + 3) = a ^ 9 * B ^ 15 (identity on both sides)
3n=9 n=3
3m+3=15 m=4

If (a ^ m * B ^ m) ^ 3 = a ^ 9 * B ^ 15, then M = (), n = ()

According to the meaning of the title:
3m=9
3n=15
The solution is m = 3, n = 5

If (ambnb) 3 = a9b15, find the value of 2m + n

∵ (am · BN · b) 3 = a3mb3nb3 = a3mb3n + 3, ∵ 3M = 9, 3N + 3 = 15, the solution is m = 3, n = 4. ∵ 2m + n = 23 + 4 = 27 = 128