Answer:
See below.
Step-by-step explanation:
4)
So we have the expression:
[tex](-6n^{-3})^2[/tex]
We can use the power of a product property, where:
[tex](ab)^n=a^n\cdot b^n[/tex]
So:
[tex]=(-6)^2\cdot(n^{-3})^2[/tex]
For the left, -6 squared is the same as -6 times -6. This equals positive 36.
For the right, we can use the power of a power property. The property says that:
[tex](a^n)^k=a^{nk}[/tex]
So:
[tex](n^{-3})^2=n^{(-3)(2)}\\=n^{-6}[/tex]
So, all together, we have:
[tex]=(-6)^2\cdot(n^{-3})^2\\=36n^{-6}[/tex]
6)
We have the expression:
[tex]-\frac{3x^0}{x^4}[/tex]
First, note that anything to the zeroth power (except for 0) is 1, thus, x^0 is also 1. Simplify:
[tex]=-\frac{3}{x^4}[/tex]
And that's the simplest we can do :)
Notes for 6)
We can put the x^4 to the numerator. Recall that when you put an exponent to opposite side, you put a negative. In other words:
[tex]x^n=\frac{1}{x^{-n}}[/tex]
And vice versa:
[tex]\frac{1}{x^{-n}}=x^n[/tex]
So, we can write the above as:
[tex]=-\frac{3}{x^4}\\=-\frac{3}{x^{-(-4)}}\\=-3x^{-4}[/tex]
However, traditionally, we want only positive exponents, so this wouldn't be correct.
