Rules of Indices

Question 1

a^m x a^n = ?

Answer 1

a^m+n

Question 2

a^m / a^n = ?

Answer 2

a^m-n

Question 3

(a^m)^n = ?

Answer 3

a^m X n

Question 4

(ab)^n = ?

Answer 4

a^n x b^n

Question 5

a^0 = ?

Answer 5

1

Question 5

(a/b)^n = ?

Answer 5

a^n / b^n

Question 6

a^-n = ?

Answer 6

1 / a^n

Question 7

a^(m/n) = two different options

Answer 7

(n SQUARE ROOT a)^m

(a^1/n)^m

Question 8

(a^x) + (a^y) = ?

Answer 8

a^(x+y)

Question 9

If you have a fraction to the power of a negative, how can you change the exponent to a positive?

Answer 9

By flipping the fraction around

Question 10

How do you find the exponent of an equation. For example

27^x = 9

Answer 10

Step 1) Re-write numbers as a common base, i.e. what are 27 and 9 multiples of….so we need a number that we can raise to the power of other numbers to equal 9 and 27.

3^3 = 27
3^2 = 9.

Step 2) Substitute these back in:
(3^3)^x = 3^2
Simplified:
3^3x = 3^2

Step 3) Now bases are equal we can remove them and just look at the exponents:
3x = 2

Step 4) From there we can solve:

x = 2/3