Simplifying Expressions with the Laws

Real expressions mix coefficients (the numbers), several variables and all the laws at once. The strategy is to deal with each part separately: numbers with numbers, and each variable with its own kind.

Worked example 1. Simplify $\dfrac{12x^5 y^3}{4x^2 y}$.

• Numbers: $12 \div 4 = 3$.
• $x$: $x^{5-2} = x^3$.
• $y$: $y^{3-1} = y^2$.

So the answer is $3x^3 y^2$.

Worked example 2. Simplify $(2a^2 b)^3$. The outside power of 3 lands on every factor: $2^3 = 8$, $a^{2\times 3} = a^6$, $b^{1\times 3} = b^3$. So $(2a^2 b)^3 = 8a^6 b^3$.