Question

I'm genuinely lost in any problems like this and my teachers are no help, I need help doing exponents in general, everything to do with them. I genuinely need help​

Answer 1

Explanation:

x^m×x^n=x^{m+n}

x^m÷x^n=x^{m-n}

`(1)/(x^m) =x^(-m)\\x^(-n)=(1)/(x^n) \\(xyz)^m=x^m* y^m * z^m \\(x^m)^n=x^(mn)`

`x^0=1`

Answer 2

See below.

Explanation:

4)

So we have the expression:

`(-6n^(-3))^2`

We can use the power of a product property, where:

`(ab)^n=a^n\cdot b^n`

So:

`=(-6)^2\cdot(n^(-3))^2`

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:

`(a^n)^k=a^(nk)`

So:

`(n^(-3))^2=n^((-3)(2))\\=n^(-6)`

So, all together, we have:

`=(-6)^2\cdot(n^(-3))^2\\=36n^(-6)`

6)

We have the expression:

`-(3x^0)/(x^4)`

First, note that anything to the zeroth power (except for 0) is 1, thus, x^0 is also 1. Simplify:

`=-(3)/(x^4)`

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:

`x^n=(1)/(x^(-n))`

And vice versa:

`(1)/(x^(-n))=x^n`

So, we can write the above as:

`=-(3)/(x^4)\\=-(3)/(x^(-(-4)))\\=-3x^(-4)`

However, traditionally, we want only positive exponents, so this wouldn't be correct.