Question

N^3 = n? × n^-3


What is the substitute for the question mark?

Answer 1

You have the expression

`n^3=n^(?)\cdot n^(-3)`

and want to find ?.

First, note the property

`n^m\cdot n^k=n^(m+k).`

Using this property, you can write

`n^(?)\cdot n^(-3)=n^(?+(-3))=n^(?-3).`

If

`n^3=n^(?-3),`

then

`3=?-3,\\ \\?-3=3,\\ \\?=3+3,\\ \\?=6.`

Answer: 6.