Question

I need help with Multiplication Properties of Exponents desperately!! I've tried to solve both problems repeatedly and I cannot solve them. I really need to redo the assignment so any help is welcome!
P.S. My teacher said on the assignment that the first one is going to be a negative.

Answer 1

Answer:

1) x= -36.

2) x = 0.

Step-by-step explanation:

1) Taking the 3rd power to both sides and using the following exponent law:

$\left(a^b\right)^c = a^{bc}$

we get:

$\left(\left(m^{x}\right)^{\frac{1}{3}}\right)^3 = \left(m^{-12}\right)^3 \\ m^x = m^{-36}$

So this tells us that x = -36.

2) We can distribute the power inside every term. So the left side becomes:

$\left(3x^3y^x\right)^3 = 3^3\left(x^3)^3y^{3x} = 27x^9y^{3x}$

Now, the trick here is to remember that $y^0 = 1$, so replacing 1 with $y^0$, which then gives us:

$27x^9y^{3x} = 27x^9y^{0}$, telling us that 3x = 0 and thus, x = 0.