Indices

• a^m×aⁿ =a^m+n

• a^m÷aⁿ =a^m–n

• (a^m)ⁿ=a^mn

• a^1/n =ⁿ√a

• a⁰=1

• a^m/n = ⁿ√a^m = (ⁿ√a)^m

• a^-n =1/aⁿ

1. a^m×aⁿ =a^m+n

(a) 5^-3×5⁴

=5^-3+4

=5¹

=5

(b) 7^-4 ×7^-2

=7^-4+-2

=7^-4-2

=7^-6

=1/7⁶

2. a^m÷aⁿ =a^m-n

(a) 3⁵ ÷3^-2

=3^{5- -2}

=3⁵⁺²

=3⁷

(b) 11^-3 ÷11^-5

=11^{-3- -5} 

=11^-3+5

=11²

=121

3. (a^m)ⁿ=a^mn

(a) (6^-3)⁴ 

=6^-3×4

=6-12

=1/6¹²

4. a^m/n = ⁿ√a^m = (ⁿ√a)^m

(a) 64^2/3

=(³√64)²

=(4)²

=16