標題:

Mathematics (With steps)

發問:

Simplify [5^3x*5^3x(3x-1)/5^x+4*5^2x-4]/25^-3x 9^2n-1*27^n+1/3^4n-1 [3d^-3*ef^-4/(-e^4f^-2)(de^-3)]/[15d^-3e^-2f/(-9ef^-2)(e2)^0 7^3x+7^3x+2 3*4^3n-2+5*8^2n/4^3n+8^2n-1 3^2n+3 +9^n+1/3^2n+1

最佳解答:

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(1) [(53x)(53(3x-1))/(5x+4)(52x-4)]/25-3x = [53x+9x-3 / 5x+4+2x-4] / 5-6x = [512x-3 / 53x]( 56x ) = 512x-3+6x / 53x = 518x-3 / 53x = 518x-3-3x = 515x-3 (2) 92n-1(27n+1)/34n-1 = 34n-2 ( 33n+3 ) / 34n-1 = 34n-2+3n+3 / 34n-1 = 37n+1 / 34n-1 = 37n+1-4n+1 = 33n+2 (3)[3d-3(ef -4)/(-e4f -2)(de-3)]/[15d-3e-2f/(-9ef -2)(e2)0] = [3d-3ef –4 / -edf –2 ] / [15d-3e-2f / - 9ef -2 ] = 3d-4f –2 / [ 5d-3e-3f-3 / 3 ] = 9d-4f –2 / 5d-3e-3f3 = 9d3e3/ 5d4f3f2 = 9e3/ 5df5 (4) 73x+73x+2 = 73x ( 1 + 72 ) = 50 ( 73x ) (5) [3(43n-2)+5(82n)] /[43n+82n-1 ] =[3(26n-4 ) + 5(26n ) ] / [ 26n + 26n-3 ] = 26n [ 3 ( 2-4 ) + 5 ] / 26n [ 1 + 2-3 ] = 83 / 18 (6) [32n+3 +9n+1]/32n+1 = [ 32n+3 + 32n+2 ] / 32n+1 = 32n [ 33 + 32 ] / 32n ( 3 ) = 12

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