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

Answer:

Step-by-step explanation:

x^m×x^n=x^{m+n}

x^m÷x^n=x^{m-n}

$\frac{1}{x^m} =x^{-m}\\x^{-n}=\frac{1}{x^n} \\(xyz)^m=x^m\times y^m \times z^m \\(x^m)^n=x^{mn}$

$x^0=1$

Answer 2

Answer:

See below.

Step-by-step 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:

$-\frac{3x^0}{x^4}$

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

$=-\frac{3}{x^4}$

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:

$x^n=\frac{1}{x^{-n}}$

And vice versa:

$\frac{1}{x^{-n}}=x^n$

So, we can write the above as:

$=-\frac{3}{x^4}\\=-\frac{3}{x^{-(-4)}}\\=-3x^{-4}$

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