Given the nth power of x = 5 and the nth power of y = 3, what is the 2n power of (XY)

Given the nth power of x = 5 and the nth power of y = 3, what is the 2n power of (XY)

(XY)^2n
=x^2n*y^2n
=(x^n)^2*(y^n)^2
=25*9
=225

If the nth power of x = 5 times the nth power of y = 2, find the 3N power of (XY)

∵x^n=5*y^n=2
∴x^n=2,y^n=2/5
(xy)^(3n)=[（xy)^n]³
=[(x^n) *（y^n)]³
=[2* 2/5]³
=(4/5)³
=64/125

If the nth power of x = 2 and the nth power of y = 5, then the nth power of (XY) = how many?

(xy)^n
=x^n*y^n
=2*5
=10

Given that the power of X of 2 is equal to the power of 5 and the power of Y is equal to 10, what is the ratio of 1 / X to 1 / y

2^x=5^y=10
xlg2=ylg5=1
x=1/lg2 y=1/lg5
1/x=lg2 1/y=lg5
1/x+1/y=lg2+lg5=lg10=1

If X-Y = 2 and the square of x plus the square of Y equals 4, what is the value of X to the 2002 power plus y to the power of 2002 If X-Y = 2, the square of x plus the square of Y is equal to 4. Find out the value of the algebraic formula x to the power of 2002 and the power of y to the power of 2002

When x = 2, x ^ 2002 + y ^ 2002 = 2 ^ 2002; when y = 2, x ^ 2002 + y ^ 2002 = 2 ^ 2002

Given that a + B + C = 0, the square of a plus the square of B plus the square of C equals 4. What is the fourth power of a plus the fourth power of B plus the fourth power of C Urgent,

a+b+c=0
(a+b+c)²=0
a²+b²+c²+2(ab+bc+ca)=0
4+2(ab+bc+ca)=0
ab+bc+ca=-2
a²+b²+c²=4
(a²+b²+c²)²=16
a^4+b^4+c^4+2(a²b²+b²c²+c²a²)=16
a^4+b^4+c^4+2[(ab+bc+ca)²-2(a²bc+ab²c+abc²)]=16
a^4+b^4+c^4+2[(ab+bc+ca)²-2abc(a+b+c)]=16
a^4+b^4+c^4+2[(-2)²-2abc•0]=16
a^4+b^4+c^4+8=16
A ^ 4 + B ^ 4 + C ^ 4 = 8

The first power of X and the second power of Y is equal to 5?

x+y^2=5
This is a quadratic equation of two variables

The square of X + X-1 = 0 is equal to the third power of X + the second power of 2x + 3

x^2+x-1=0
x^2+x=1
x^3+2x^2+3
=x^3+x^2+x^2+3
=x(x^2+x)+x^2+3
=x*1+x^2+3
=x^2+x+3
=1+3
=4

The square of a + A + 1 = 0. How much is the fifth power of a + the fourth power of a + the third power of a + the second power of a + A + 5?

Square of a + A + 1 = 0
The 5th power of a + the 4th power of a + the 3rd power of a + the 2nd power of a + A + 5=
(the 5th power of a + the 4th power of a + the 3rd power of a) + (the 2nd power of a + A + 1) + 4=
The third power of a * (the square of a + A + 1) + (the second power of a + A + 1) + 4=
The third power of a * 0 + 0 + 4=
Four

Given that the square of x minus x minus 1 is equal to 0, find the value of the third power of negative x plus 2x plus 2011

-X3+2X+2011
=-(X3+1)+2X+2012
=-(X+1)(X2-X+1)+2X+2012
Because x2-x-1 = 0, then x2-x = 1 is substituted into the above formula, then:
Original formula = - 2x-2 + 2x + 2012 = 2010