Zjednodušiť túto otázku zákona o indexe?

odpoveď:

# ((- 2.xy) ^ 2 * 2 (x ^ 2y) ^ 3) / (8 (xy) ^ 3) = x ^ 5R ^ 2 #

vysvetlenie:

zákony:

# (X * y) ^ a = x ^ a * y ^ a #

# (X ^ a) ^ b = x ^ (a * b) #

# X ^ a * x ^ b = x ^ (a + b) #

# (X ^ a) / (x ^ b) = x ^ (a-b) #

# ((- 2.xy) ^ 2 * 2 (x ^ 2y) ^ 3) / (8 (xy) ^ 3) #

# = ((- 2) ^ 2 x ^ 2r ^ 2 * 2x ^ (2 x 3) y ^ 3) / (8x ^ 3r ^ 3) #

# = (4x ^ 2r ^ 2 * 2x ^ 6Y ^ 3) / (8x ^ 3r ^ 3) #

# = ((4 * 2) (x ^ 2 * x ^ 6) (y ^ 2 * y ^ 3)) / (8x ^ 3r ^ 3) #

# = ((8), (x ^ (2 + 6)) (y ^ (2 + 3))) / (8x ^ 3r ^ 3) #

# = ((8), (x ^ (8)), (y ^ (5))) / (8x ^ 3r ^ 3) #

# = (8/8) ((x ^ 8) / (x ^ 3)) ((y ^ 5) / (y ^ 3)) #

# = (1) (x ^ (8-3)), (y ^ (5-3)) #

# = (X ^ (5)), (y ^ (2)) #

# = X ^ 5R ^ 2 #