simplify the following expression:  3 z ^ 4 t ^ 3 / z ^ 2 t q ^ 0?
367922
the answer is 3 z^2 t^2 because q^0 is equal to 1, like all numbers raised to the zero power, and then when you divide the  variable with the exponents you simply subtract them. This means that something like t^5 / t^3 is equals to t^2. Hope this helps.
968026
I got   3(x² - 5x + 4) or 3( x - 4 )( x - 1 )\n\nLet me show you my work...\n\n3( x - 2 )² - 3(x - 2) - 6\n\nSimplify\n\n3( x -2 )( x - 2 ) - 3( x- 2 ) - 6\n\nDistribute\n\n3( x² - 4x + 4) - 3x + 6 - 6\n\nDistribute and Simplify\n\n3x² - 12x + 12 - 3x\n\nSimplify\n\n3x² - 15x + 12\n\nYou can now simplify by factoring out 3\n\n3(x² - 5x + 4)\nor\n3( x - 4 )( x - 1 )
753930
The most intuitive way to answer is to use Gauss-Jordan elimination, as described below.\n\n\nw + x + y + z = 24\n3w + 3x + 3y + 3z = 72\n3w - 2x - 3y + 3z  = -9\n5x + 6y= 81\n\nw + x + y + z = 24\n5w + 5x + 5y + 5z = 120\n5w + 3x - 2y - 2z  = 4\n2x + 7y + 7z = 116\n\nw + x + y + z = 24\n2w + 2x + 2y + 2z = 48\n2w + 4x + 4y - 5z  = 22\n-2x - 2y + 7z = 26\n\n2x + 7y + 7z = 116\n-2x - 2y + 7z = 26\n\n4x + 9y = 90\n5x + 6y= 81\n\n20x + 45y = 450\n20x + 24y = 324\n21y = 126\n\ny = 6\n\n4x + 9y = 90\n4x + 54= 90\n4x  = 36\nx = 9\n\n2x + 7y + 7z = 116\n18 + 42 + 7z = 116\n7z = 56\nz = 8\n\nw + x + y + z = 24\nw + 9 + 6 + 8 = 24\nw = 1\n{w,x,y,z} = {1,9,6,8}\n\nAnother method is to put the coefficiants into a matrix, and put it into reduced-row echelon form.\n\n|1 1   1  1  24|\n|3  -2 -3 3 -9|\n|5  3  -2 -2 4|\n|2  4  4  -5 22|\n\nIn RREF...\n|1 0 0 0 1|\n|0 1 0 0 9|\n|0 0 1 0 6|\n|0 0 0 1 8|\n\nThese are all new valid equations, just in a much nicer form. Specially, 1w+0x+0y+0z=1, etc.\nThis tells us that w=1, x=9, y=6, and z=8.\n\nAlso, you could use Cramer's rule with these equations and get the same answer, but I will not demonstrate that one.
439090
((x^2-2x)/4y)/((x^2-4)/6)\n=(6x(x-2))/(4y*(x-2)(x+2))\n=3x/(2y(x+2))
696447
taking out common factors,the expression\n=3xy(4x-3x^4y-5y^3)/3xy\n=4x-3x^4y-5y^3
920343
(4/3)[x^3/(2-x)]^(1/3)\n[(2-x)(3)x^2-x^3(-1)]/\n(2-x)^2=\n\n 4x[1/(2-x)]^(1/3)\n[3x^2(2-x)+x^3]/\n3(2-x)^2
919306
3m^1/6 n^1/3 over 4n^-2/3 all to ^2\n= ( 3m^1/6 n^1/3 / 4n^-2/3 )^2\n= (3 m^1/6 n^{1/3+2/3} /4 )^2\n= (9/16) m^{2/6} n^2\n= (9/16) m^{1/3} n^2 '
791199
(6x^2)/4x^2y-12xy(x^2+x-12)/3x^2+12x\n3/(2y)-4y/x(x^2+x-12)+12x\n=(3/2y)-(4x^2y-4xy+48y)/x+12x\n=[3x-2y(4x^2y-4xy+48y)+24x^2y]\n/2xy\n=[3x-8x^2y^2+8xy^2-96y^2\n+24x^2y]/2xy
643397
(8y^3 + 27)/(2xy - 10y + 3x - 15)\n((2y + 3)(4y^2 - 6y + 9))/((2xy - 10y) + (3x - 15))\n((2y + 3)(4y^2 - 6y + 9))/(2y(x - 5) + 3(x - 5))\n((2y + 3)(4y^2 - 6y + 9))/((2y + 3)(x - 5))\nthe (2y + 3)s cancel out\n(4y^2 - 6y + 9)/(x - 5)\n\nANS : (4y^2 - 6y + 9)/(x - 5)
741312
If f(t)=(t-a)*(t-b) = t^2-(a+b)*t+ab; then \nI=(1/3)*t^3 - (a/2+b/2)*t^2 + a*b*t+C
917114
√45x^6y^7=√(3x^3y^3)^2*5y=3x^3y^3√5y
184147
5t(t^2+t-1)(t^3-t^2+2t+2)\nIts a long answer but it's CORRECT.
697247
C = (W^2*L^2) / (24T^2)\nC(24T^2) = W^2*L^2\n[C(24T^2)]/L^2 = W^2\nAnswer:\nW = sq.rt {[C(24T^2)]/L^2}
423853
[2x^{2}+ 2x2y]+[2x2y+2x^{2}]+\n[6yz^{9}+3y^{2}9z^{8}]+\n[3y9z^{8}+y^{3}72z^{7}]\n\nthis is using z as the last term.  Based on what I used, I think a 3D parabola of sorts will emerge
966462
(6x^2)/(4x^2 y-12xy) * (x^2 + x - 12)/ (3x^2 + 12x)\n\nFirst, I would attempt to simplify if possible:\n2x(3x)/x(2xy-6y) * (x^2 + x - 12)/ (3x^2 + 12x )\n(3x) / (2xy - 6y) * (x^2 + x - 12)/ (3x^2 + 12x)\n\nRewrite to see if we can cross cancel:\n\n(3x)           (x^2 + x - 12)\n---------  *   -----------------\n(2xy-6y)    (3x)(x + 4x)\n\n1               (x^2 + x - 12)\n---------- *  -----------------\n(2xy-6y)     (x+4x)\n\nUnfoil the (x^2 + x -12 to see if we can further simplify\n\n(x^2 + x - 12) = (x -3)(x+4) so you will have:\n\n1             (x-3)(x+4)\n-------  *  --------------\n2y(x-3)      (x+4)\n\nBy simplification:\n\n1           (x-3)\n------   * ----------\n2y(x-3)     1\n\nBy Cross Cancel:\n1/2y
352749
By the chain rule:\n[e^(3x^(2)-7x)]*(6x-7)
879176
= x(x+3) + 4(x+3)\n= x^2 + 3x +4x + 12\n= x^2 +7x + 12