Fully simplify (8a^2b * ab^4)/(2a^3b^2)

8a³bab⁴ 2a³b² (can write this more clearly by hand using whiteboard) First go about seperating and collecting terms. Begin with the top line. 8 remains the same as there are no other known numbers. We have 2 a terms so we can collect them together, remembering that a value with no exponent (index) written means the exponent is 1. Apply laws of powers means we have a³⁺¹ on our top row. Repeat the same for b to obtain fully 8a³⁺¹b¹⁺⁴ = 8a⁴b⁵. Now we have simplified the top row we can use the bottom row to obtain our answer. Remembering that when dividing instead of adding the exponents you divide them. Working through each term we see that 8/2 = 4,  a⁴/a³ = a^4-3,  b⁵/b² = b^5-2 From this we obtain our answer of 4ab³ (N.B. this question is aimed at higher students who already understand the laws of powers and their origins. Students at foundation level or those recieving tuition at the start of the year rather than in the run up to exams may require an explanation of the origin of these laws to provide deeper understanding eg a³ = aa*a)