Indices

Rule:

1. a^m × aⁿ = a^m+n
2. a^m / aⁿ = a^m-n
3. (a^m)ⁿ = a^mn
4. (ab)^m = a^mb^m
5. (a/b)^m = a^m/b^m
6. a⁰ = 1
7. if a^m = aⁿ, then m = n
8. a^m = k, then a = k^1/m

Exercise

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