The Laws of Indices, which apply to numbers, are also applied to algebra. Consider y3 x y2.
The term y3 can be expanded to y x y x y. The other term, y2, can be expanded to y x y. Therefore y3 x y2 = y x y x y x y x y, which is equal to y5.
This can be written as ya x yb = y(a + b). When multiplying the same variable, add the powers.
Note that the variable letter must be the same for both the terms being multiplied.
Division works in a similar way. The rule is written as ya ÷ yb = y(a - b). When dividing the same variable, subtract the powers. The example e6 ÷ e3 can be shown as:
= `frac(e times e times e times e times e times e)(e times e)`
= `frac(e times e times e times e)(1)`
The division rule leads to the fact that e0 = 1. This can be shown by e2 ÷ e2 = e2 - 2 = e0.
1. Simplify x3 x 4x3.
x3 x 4x3 = 4 x x(3 + 3) = 4x6
2. Simplify 4a5b ÷ 2a3
Calculate the numbers: 4 ÷ 2 = 2.
Calculate the variable a: a5 ÷ a3 = a(5-3) = a2
The variable b is not divided.
Put it all together: 2a2b