Step by step
The question
Question: simplify (3a²b)³.
(3a2b)3
1 Power of a product
The rule: a power outside a bracket goes on each part inside.
And for a power of a power, we multiply the powers.
(ab)n = anbn
(xa)b = xa × b
So each part inside gets the power 3.
= 33(a2)3b3
3³ is 3 times 3 times 3, which is 27.
33 = 3 × 3 × 3
= 27
So 3³ becomes 27.
For a² to the power 3, we multiply the powers.
= 27a2 × 3b3
2 times 3 is 6.
So we get 27a⁶b³.
= 27a6b3
Answer
= 27a6b3