Review Material -- Exponents

**Mad** · February 10th 2008, 10:51 AM

I just started Pre-Calc last week and am already stuck. I added the course late (college freshman) and consequently missed three classes. Those three classes were, apparently, focused on reviewing College Algebra.

Now, I liked Algebra, I did. I did really well in it too but I haven't had it in four or five years. As a result, I've forgotten a lot of what I once knew. Unfortunately, the professor did a lot of the work in class but because I wasn't there, I have to get the answers myself.

If someone could help me, I should be fine. I just need some reminders.

(a^2/b^3)^-2

x^2y^-4/x^-5y^-2

[(x/y)^-2]^3

All of the exponents are to be positive.

I think I can do the rest of the review packet on my own.

**Jhevon** · February 10th 2008, 11:16 AM

Originally Posted by Mad

(a^2/b^3)^-2

reminder 1: $\left( \frac xy \right)^a = \frac {x^a}{y^a}$ , which means, $\left( \frac {x^a}{y^b} \right)^c = \frac {x^{ac}}{y^{bc}}$ , because...

reminder 2: $(x^a)^b = x^{ab}$

so here: $\left( \frac {a^2}{b^3} \right)^{-2} = \frac {a^{2(-2)}}{b^{3(-2)}} = \frac {a^{-4}}{b^{-6}}$

now we want positive powers, so reminder 3: $x^{-a} = \frac 1{x^a}$ , so...

$\frac {a^{-4}}{b^{-6}} = \frac {b^6}{a^4}$

x^2y^-4/x^-5y^-2

reminder 4: $\frac {x^a}{x^b} = x^{a - b}$

reminder 5: $x^a \cdot x^b = x^{a + b}$ (of course, by $\cdot$ i mean multiply)

so, $\frac {x^2 y^{-4}}{x^{-5}y^{-2}} = x^{2 - (-5)}y^{-4 - (-2)} = x^7y^{-2} = \frac {x^7}{y^2}$

[(x/y)^-2]^3

try this one. i reminders i gave in the first problem should be a big help

**Mad** · February 10th 2008, 11:52 AM

$y^6/x^6$

Is that right?

**Jhevon** · February 10th 2008, 12:03 PM

Originally Posted by Mad

$y^6/x^6$

Is that right?

yes!

or i don't know if you would prefer to write $\left( \frac xy \right)^6$

**Mad** · February 10th 2008, 12:06 PM

Thanks. ^_^

**Mad** · February 11th 2008, 05:42 PM

(3a^2b^-2c^-1/27a^-1b^2c^-4)^-2

$9a^2c^10/b^8$

(2^-1x^2y^-3/4x^-2 y^-5)^-2

I'm not quite sure what do to with that second one.

Wait, is it $1/y^16$ ?

**earboth** · February 12th 2008, 04:17 AM

Originally Posted by Mad

... I just need some reminders.

...

Try to do your question with the help of the attached brain crutch

**earboth** · February 13th 2008, 10:35 AM

Originally Posted by Mad

(3a^2b^-2c^-1/27a^-1b^2c^-4)^-2

$9a^2c^10/b^8$ ...
sorry but no

(2^-1x^2y^-3/4x^-2 y^-5)^-2

Wait, is it $1/y^16$ ?

#1:

$\left(\frac{3a^2 \cdot b^{-2} \cdot c^{-1}}{27a^{-1} \cdot b^2 \cdot c^{-4}}\right)^{-2} = \left(\frac19 \cdot a^3 b^{-4} c^3\right)^{-2} = 81 a^{-6} b^8 c^{-6}$

#2:

$\left(\frac{2^{-1} x^2 y^{-3}}{4x^{-2} y^{-5}}\right)^{-2} = \left(2^{-3} x^4 y^2\right)^{-2} = 2^6 x^{-8} y^{-4}$

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