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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​

I'm genuinely lost in any problems like this and my teachers are no help, I need help-example-1
User Bartezr
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2 Answers

4 votes

Answer:

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

User Bergben
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7.8k points
5 votes

Answer:

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.

User Madcow
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7.3k points

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