Question

Please help me! Hint: the number is negative

Answer 1

Answer:

$-36$ goes into the box

Step-by-step explanation:

Let the number be $x$,  then

$(m^x)^{\frac{1}{3}}=m^{-12}$

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;

$m^{x\times \frac{1}{3}}=m^{-12}$

$\Rightarrow m^{\frac{x}{3}}=m^{-12}$

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

${\frac{x}{3}=-12$

We now multiply both sides by 3 to get;

$\frac{x}{3}\times 3=-12\times 3$

$\Rightarrow x =-36$

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