We previously looked at how to raise fractions to a power. In this chapter we are going to extend that concept to include algebraic fractional bases.
For any base number of the form $$ab, and any number $$n as a power,
$$(ab)n=anbn
If $$n happens to be negative, then we also use the fact $$a−n=1a. This gives us the following rule:
$$(ab)−n=(ba)n
For example, the expression $$(xy)2 can be expanded in the following way: $$xy×xy=x×xy×y$$=$$x2y2. This shows that $$(xy)2=x2y2
Similarly, an expression like $$(3x2y)3 expands to $$3x×3x×3x2y×2y×2y=27x38y3. This shows that $$(3x2y)3=27x38y3.
Practice questions
Question 1
Rewrite the following using an exponent law.
$$(ab)3=()()
Question 2
Simplify, and evaluate where possible, the following expression:
$$(8b)−2
Question 3
Simplify, and evaluate where possible, the following expression:
$$(3n6)3