Question

What is the simplified form of the expression? q^33/4/q^8

A. q^1/4

B.q^66

C.1/q^1/4

D. 1/q^66

Answer 1

`Use:(a^n)/(a^m)=a^(n-m)\\\\\frac{q^{(33)/(4)}}{q^8}=q^{(33)/(4)-8}=q^{8(1)/(4)-8}=q^(1)/(4)`

Answer: A. q^1/4

Answer 2

The answer is A.
`q^(1)/(4)`

Explanation:

Firstly, we have to express the division of both numbers:

`(q^(33)/(4) )/(q^(1)/(4) )`.

We need to applicate the properties of power numbers. When two power numbers are being divided and they have the same base, the base remains and the powers is subtract each other. In general:

`(b^m)/(b^n) =b^(^m^-^n^)`

So, If we applicate this property:

`(q^(33)/(4) )/(q^(1)/(4) )`

`q^(^(33)/(4) ^-^8 ^)\\q^(^(33-32)/(4)^)\\q^(^(1)/(4)^)`

Finally, the simplified form is
`q^(1)/(4)`