Suppose we want to divide

6x
^{
3
}
÷ 2x

We first factorise 6x
^{
3
}
÷ 2x separately

6x
^{
3
}
= 6 × x
^{
3
}

= 2 × 3 × x × x × x

2x = 2 × x

And then, divide

(6x
^{
3
}
)/2x = (2 × 3 × x × x × x)/(2 × x)

= 3 × x × x

= 3x
^{
2
}

Let’s do some more examples

###
6x
^{
3
}
÷ 3x
^{
2
}

Factorising 6x
^{
3
}
÷ 3x
^{
2
}
separately

6x
^{
3
}
= 6 × x
^{
3
}

= 2 × 3 × 𝑥 × 𝑥 × 𝑥

3x
^{
2
}
= 3 × x
^{
2
}

= 3 × 𝑥 × 𝑥

Dividing

(6x
^{
3
}
)/(3x
^{
2
}
) = (2 × 3 × x × x × x)/(3 × x × x)

= 2𝑥