Indices

Question 1

What is equal to:

a) x^-n
b) (x^m)ⁿ
c) x⁰
d) x¹
e) (x^m) x (xⁿ)
f) x^m/xⁿ
g) x^1/n
h) x^m/n

Answer 1

a) 1/xⁿ
b) x^mn
c) 1
d) x
e) x^m+n
f) x^m-n
g) ⁿ(square root of x)
h) (x^1/n)^m = (x^m)^1/n

Question 2

What’s do you do to turn a negative indice into a positive one when considering fractions?

Answer 2

Switch the denominator and the numerator around

eg. (9/16)^-1/2 = (16/9)^1/2 = the square root of 16/9 = the square root of sixteen over the square root of 9 = 4/3

Question 3

What is the strategy for finding the letter in an indices question? Make a common base

The square root of 8 = 2^x

find x.

Make a common base ie. the square root of 2³ = 2^x (in this case, the common base is 2).

So = (2³)^1/2 = 2^3/2 = 2^x

x = 3/2