1. ## Exponent confusion.

Um. i was out the day of the lesson for this assignment, and i read the book's lesson, but it doesn't explain everything. Basically, it says
$\displaystyle a^3 • a^2 = a • a • a • a • a = a^5$
so i learn that a^3 • a^2 (in this situation) is basically adding the exponents. no problem.
then it says...
$\displaystyle (3^5)^2 = 3 to the power of 10$
ok, so you multiply parethetical exponents and outside exponents. again, nothing difficult.
then it says..
$\displaystyle (6 • 5)^2 = 6^2 • 5^2 = 36 • 25 = 900$
add the exponent to everything in parenthesis. again, easy.
but then you get to the problems...
$\displaystyle (3b)^3 • b$
um. so like, you have 3b^3, and multiply it by 1b? so it's... still 3b^3? or did i mess up somewhere?
$\displaystyle 5^3 • (5a^4)^2$
5^3=125, so it's 125 • ...5a^8? or 5a^6? @_@
$\displaystyle 4x • (x • x^3)^2$
buhhh.... 4x • (x^4)^2.. 4x • x^8... 4x^8?

there's more confusing ones, but hopefully i can sort most of them out if i get these figured out...thanks

2. Originally Posted by Forkmaster
then it says..
$\displaystyle (6 • 5)^2 = 6^2 • 5^2 = 36 • 25 = 900$
um, that's wrong, unless you have a typo. as in, you meant to write $\displaystyle (6 \cdot 5)^2$

use the command \cdot to put the multiplication dot in... you can't post images in LaTeX and expect them to work.

$\displaystyle (3b)^3 • b$
um. so like, you have 3b^3, and multiply it by 1b? so it's... still 3b^3? or did i mess up somewhere?
do one piece at a time.

so we have $\displaystyle (3b)^3b$

work out the cubed part first, we get:

$\displaystyle (3^3 b^3)b = (27b^3)b$

now multiply the b's, using the first rule you posted

you get: $\displaystyle 27b^4$

now try the others

3. Originally Posted by Forkmaster
Um. i was out the day of the lesson for this assignment, and i read the book's lesson, but it doesn't explain everything. Basically, it says
$\displaystyle a^3 • a^2 = a • a • a • a • a = a^5$
so i learn that a^3 • a^2 (in this situation) is basically adding the exponents. no problem.
then it says...
$\displaystyle (3^5)^2 = 3 to the power of 10$
ok, so you multiply parethetical exponents and outside exponents. again, nothing difficult.
then it says..
$\displaystyle (6 • 5)^2 = 6^2 • 5^2 = 36 • 25 = 900$
add the exponent to everything in parenthesis. again, easy.
but then you get to the problems...
$\displaystyle (3b)^3 • b$
um. so like, you have 3b^3, and multiply it by 1b? so it's... still 3b^3? or did i mess up somewhere?
$\displaystyle 5^3 • (5a^4)^2$
5^3=125, so it's 125 • ...5a^8? or 5a^6? @_@
$\displaystyle 4x • (x • x^3)^2$
buhhh.... 4x • (x^4)^2.. 4x • x^8... 4x^8?

there's more confusing ones, but hopefully i can sort most of them out if i get these figured out...thanks
These exponent rules are merely a way of counting factors. Count the number of factors of a in the following "laws" in order to get the rules.
$\displaystyle a^m = \begin{array}{c} \underbrace{(a \cdot a \cdot ~ .... ~ \cdot a)} \\ \text{m times} \end{array}$

$\displaystyle a^m \cdot a^n = \begin{array}{c} \underbrace{(a \cdot a \cdot ~ .... ~ \cdot a)} \\ \text{m times} \end{array} \cdot \begin{array}{c} \underbrace{(a \cdot a \cdot ~ .... ~ \cdot a)} \\ \text{n times} \end{array}$$\displaystyle = \begin{array}{c} \underbrace{(a \cdot a \cdot ~ .... ~ \cdot a)} \\ \text{m + n times} \end{array} = a^{m + n}$

$\displaystyle (a^m)^n = \begin{array}{c} \underbrace{a^m \cdot ~ ... ~ \cdot a^m} \\ \text{n times} \end{array} = \begin{array}{c} \underbrace{(a \cdot a \cdot ~ .... ~ \cdot a)} \\ \text{mn times} \end{array} = a^{mn}$

$\displaystyle (ab)^m = a^mb^m$
(You can sketch that one out yourself.)

So let's take apart one of your problems.
$\displaystyle (3b)^3 \cdot b$

$\displaystyle = (3^3b^3)b = 3^3 \cdot b^3 \cdot b$

$\displaystyle = 27(b^3 \cdot b^1) = 27b^{3 + 1} = 27b^4$

Always do the parenthesis first.

-Dan

4. For $\displaystyle (3b)^3 • b$:

You can split it into $\displaystyle (3^3) (b^3) (b^1)$ Remember that 3 and b are separate terms in parenthesis, you need to cube both of them.

For $\displaystyle 5^3 • (5a^4)^2$:

Again, 5 and $\displaystyle a^4$ are separate terms, so you need to square both of them, giving you:

$\displaystyle (5^3)(5^2)(a^8)$

5. Originally Posted by Jhevon
um, that's wrong, unless you have a typo. as in, you meant to write $\displaystyle (6 \cdot 5)^2$
yes, i meant to do the math dot. im new to the LaTex thing :P.

thanks for the quick replies. i think i got it now, figured out a few on my own..here's hoping that there's no suckerpunch ones that have entirely new content like this book tends to do, lol

6. Found another one that confused me a bit, but only in one place.
$\displaystyle (-ab)(a^2b)^2$
distribute the ^2 in the second parenthesis...
$\displaystyle (-ab)(a^4b^2)$
now multiply them together...
the b becomes b^3, but what of the a?
-a • a^4...
would it be a^3? -a^4? a to the power of -4? i'm confused.

7. Originally Posted by Forkmaster
Found another one that confused me a bit, but only in one place.
$\displaystyle (-ab)(a^2b)^2$
distribute the ^2 in the second parenthesis...
$\displaystyle (-ab)(a^4b^2)$
now multiply them together...
the b becomes b^3, but what of the a?
-a • a^4...
would it be a^3? -a^4? a to the power of -4? i'm confused.
you can think of $\displaystyle -a \cdot a^4$ as $\displaystyle -1 \cdot a \cdot a^4$

so now, just multiply the a's as normal, and then apply the minus 1

8. Got it. Thanks.