Step by step
The question
Question: simplify 8a³b⁵ over 2ab².
8a3b52ab2
1 Numbers and letters apart
We split it: numbers over numbers, and each letter over the same letter.
Fractions next to each other mean times.
= 82 a3a b5b2
2 Cross out
We write the powers out.
a³ is 3 a's on top.
a is 1 a's on the bottom.
= 82 b5b2aaaa
a/a is 1.
Each a on top crosses out one a on the bottom.
1 pair crosses out.
2 a's are left on top.
The rule: same letter, divide, take away the powers.
aa = 1
3 − 1 = 2
xaxb = xa − b
8/2 is 4.
So we get 4a²b³.
= 4a2b3
Let's look back.
First: numbers and letters apart.
Last: cross out.
Answer
= 4a2b3