Question

Simplify the following using law of indices. a) 12x⁷ ÷ 4x³

b) (2x)² × (2x)³ × (2x)⁵
​

Answer 1

a) 3
`x^(4)`

b) 1024
`x^(10)`

Explanation:

`(12x^(7) )/(4x^(3) )`

`(3(4)xxxxxxx)/(4xxx)` We can cancel out a 4 and 3 x's. That leaves

3xxxx

or 3
`x^(4)`

`(2x)^(2)` x
`(2x)^(3)` x
`(2x)^(5)` can be written in expanded form

[(2)(2)xx] x [(2)(2)(2)xxx] x [(2)(2)(2)(2)(2)xxxxx]

(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)xxxxxxxxxx

1024
`x^(10)`