Step by step
The question
Question: simplify x⁵ over x².
x5x2
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Cross out
We write the powers out.
x⁵ is 5 x's on top.
x² is 2 x's on the bottom.
= xxxxxxx
x/x is 1.
Each x on top crosses out one x on the bottom.
2 pairs cross out.
3 x's are left on top.
The rule: when we divide the same letter, we take away the powers.
xx = 1
5 − 2 = 3
xaxb = xa − b
So we get x³.
= x3
2 Pick the choice
Our answer is x³.
That is choice B.
B) x3
3 Why not the others
A is x⁷.
Wrong: 5 + 2: dividing takes away, 5 − 2.
A) x7 ✗ 5 + 2: dividing takes away, 5 − 2
C is x².5.
Wrong: 5 ÷ 2: divided the powers.
C) x2.5 ✗ 5 ÷ 2: divided the powers
D is 1/x³.
Wrong: 2 − 5: took away the wrong way round.
D) 1x3 ✗ 2 − 5: took away the wrong way round
Let's look back.
First: cross out.
Then: pick the choice.
Last: why not the others.
Answer
= x3