EndersWorld:

I’m confused *^*

8 months ago
EndersWorld:

$(-x^2y^{-7}z^1)^2/] 8 months ago EndersWorld: Uhhhh... 8 months ago Hero: \[(-x^2y^{-7}z^1)^2$

8 months ago
EndersWorld:

$(-x^2y^{-7}z^1)^2$

8 months ago
EndersWorld:

Yea, that

8 months ago
Hero:

First thing I would do since the whole thing is squared is this: $$(-x^2y^{-7}z^1)^2 = (-x^2y^{-7}z^1)(-x^2y^{-7}z^1)$$

8 months ago
Hero:

Hopefully you understand why that is necessary.

8 months ago
EndersWorld:

Multiply everything?

8 months ago
Hero:

Basically if you see a 2 outside the parentheses, it means to multiply whatever is in the parentheses twice.

8 months ago
Hero:

The next step is to pair like terms together: $$(-x^2y^{-7}z^1)^2 = (-x^2y^{-7}z^1)(-x^2y^{-7}z^1)$$ $$=(-x^2)(-x^2) \cdot (y^{-7})(y^{-7})\cdot(z^1)(z^1)$$

8 months ago
EndersWorld:

Aren’t the two z’s useless because they are $^1$ so they equal 1?

8 months ago
Hero:

And then go from there. There are three things to know how to do 1. How to multiply two negative numbers 2. How to multiply two exponents 3. How to multiply negative exponents

8 months ago
Hero:

Only in division will $$\dfrac{z}{z} = 1$$. Multiplying two $$z$$'s is different.

8 months ago
EndersWorld:

Two negatives multiplying is a positive. And I believe you add the exponent.

8 months ago
Hero:

Sounds good so far. What do you do with the negative exponents?

8 months ago
EndersWorld:

You add them and flip the sign to positive

8 months ago
Hero:

Actually, here's the rule for negative exponents: $$a^{-b} = \dfrac{1}{a^b}$$ In other words, expressions with negative expressions get converted to fractions.

8 months ago
EndersWorld:

That sounds... terrifying and painful..

8 months ago
Hero:

It's neither painful or terrifying. Simply a rule to apply.

8 months ago
EndersWorld:

So... $\frac{ 1 }{ y^7}$

8 months ago
Hero:

yes $$y^{-7} = \dfrac{1}{y^7}$$

8 months ago
EndersWorld:

So I have it set up, now do I just combine like terms?

8 months ago
Hero:

Yes, go ahead and attempt to finish this. Post your result below.

8 months ago
EndersWorld:

$x^4\frac{ 1 }{ y ^{14}}$

8 months ago
Hero:

What happened to the z's? I tried to help you understand that you don't eliminate them. The rule for adding adding exponents still apply to the z's

8 months ago
EndersWorld:

I told you I’m not the brightest LOL

8 months ago
EndersWorld:

No spamming :0 $x^4\frac{ 1 }{ y^14}z^2$

8 months ago
Hero:

When you express the result it should be expressed as one fraction with all the appropriate expressions in the numerator and denominator of the fraction.

8 months ago
Hero:

Remember that $$a \times \dfrac{1}{b} = \dfrac{a}{b}$$

8 months ago
Hero:

@EndersWorld I'm giving you an opportunity to express the result in the correct form.

8 months ago
EndersWorld:

$\frac{ x^4z^2 }{ y^14 }$

8 months ago
Hero:

\frac{ x^4z^2 }{ y^{14} }

8 months ago
Hero:

^Showing you the correct $$\LaTeX$$ format for your expression.

8 months ago
Hero:

Which produces this: $$\dfrac{ x^4z^2 }{ y^{14} }$$

8 months ago
EndersWorld:

So I was right :0

8 months ago
Hero:

Technically yes. Great job.

8 months ago
Hero:

Hopefully doing that one helped clear up some of your "confusion"

8 months ago
EndersWorld:

Got a different type of radical next.

8 months ago