Question

Please help me!
Hint: the number is negative

Answer 1

`-36` goes into the box

Explanation:

Let the number be
`x`, then

`(m^x)^{(1)/(3)}=m^(-12)`

We now use the following property of exponents to simplify the left hand side of the equation.

`(a^m)^n=a^(mn)`

This implies that;

`m^{x* (1)/(3)}=m^(-12)`

`\Rightarrow m^{(x)/(3)}=m^(-12)`

Since the bases are the same, we equate the exponents to get;

`{(x)/(3)=-12`

We now multiply both sides by 3 to get;

`(x)/(3)* 3=-12* 3`

`\Rightarrow x =-36`

Therefore the number that goes into the box is
`-36`