Indices

Rule:

a^m × aⁿ= a^m+n
a^m / aⁿ= a^m-n

(a^m)ⁿ= a^mn
(ab)^m= a^mb^m
(a/b)^m= a^m/b^m
a⁰= 1
if a^m = aⁿ, then m = n
a^m = k, then a = k^1/m

Exercise

Find the value of 256^0.16 × 256^0.9?
Find the value of (0.01024)⁵?
Find the value of (x^a/x^b)^1/ab × (x^b/x^c)^1/bc × (x^c/x^a)^1/ca ?
If 3^x+8 = 27^2x+1, then find the value of x.
If x = 10²⁴, y = 10⁷², x^z = y² then find the value of z.
If a^x = b^y = c^z and b²= ac, then find the value of y.