Wat is (s ^ 8t ^ -1u ^ 0 * stu ^ -8) / (s ^ -7t ^ -1u ^ 4)?

Antwoord:

# S ^ 16tu ^ -12 #

Uitleg:

wetten van indices:

# a ^ m / a ^ n = a ^ (m-n) #

# a ^ m * a ^ n = a ^ (m + n) #

# a ^ 0 = 1 #

# s ^ 8 / s ^ (- 7) = s ^ (8 - (- 7)) = s ^ 15 #

# t ^ -1 / t ^ -1 = t ^ (- 1 - (- 1)) = t ^ 0 #

# t ^ 0 = 1 #

# u ^ 0 = 1 #

#u ^ (- 8) / u ^ 4 = u ^ ((- 8) -4) = u ^ -12 #

annuleren:

# (S 8t ^ ^ ^ 0 * -1u stu ^ -8) / (^ s ^ -7t -1u ^ 4) #

# (S 15cancel ^ (t ^ -1) te annuleren (u ^ 0) * stud ^ -12) / (annuleren (s ^ -7) annuleren (t ^ -1) te annuleren (u ^ 4)) #

dan blijven we achter # 15 s ^ * s * t * u ^ -12 #

# s ^ 15 * s = s ^ 15 * s ^ 1 = s ^ (15 + 1) = s ^ 16 #

# s ^ 15 * s * t * u ^ -12 = s ^ 16 * t * u ^ -12 = s ^ 16tu ^ -12 #