פשט את שאלת חוק האינדקס?

תשובה:

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

הסבר:

חוקים:

# (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) #

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

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

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

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

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

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

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

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

# = (x ^ (5)) (y ^ (2)) #

# = x ^ ^ 5y ^ 2 #