Question

Walk through dividing monomials with me? I have a lot of trouble with it :(

Answer 1

I give medals! If that matters

Answer 2

monomial means a "bunch" of letters or numbers multiplied together.
Example:
\(2x^2y\)

if you divide, you can sometimes simplify.
\[ \frac{2 x^2 y}{2z} \]

just look at the numbers (the 2)
2/2 is 1
so you simplify to get
\[ \frac{1 x^2 y}{z} \]
we normally do not bother to write the 1 (1 times anything does not change the number), so we write
\[ \frac{x^2 y}{z} \]

Answer 3

I we had \[(\frac{ 3a^5 }{ b^3 })^2\]

Answer 4

Oh okay that makes sense, but If i had that then I would distribute it to all the numbers and variables right so it'd be\[(3^1)^2 (a^5)^2 and (b^3)^2\]

Answer 5

yes?

Answer 6

yes. there are a few ways to think of (or do this) problem.
what you wrote is true.

But it is always helpful to remember what the exponent 2 means: multiply by itself twice.

so you could also write
\[ \left(\frac{ 3a^5 }{ b^3 }\right)^2 = \left(\frac{ 3a^5 }{ b^3 }\right)\left(\frac{ 3a^5 }{ b^3 }\right)\]

Answer 7

Okay, I got you ^^

Answer 8

now multiply top times top and bottom times bottom
\[ \frac{3a^5 \cdot 3 a^5}{b^3 \cdot b^3 } \]
you "add exponents" if you have the same base, but we could go back to the definition
b^3 = b*b*b
and b^3 * b^3 is b*b*b * b*b*b
and we can use exponents to write b*b*b * b*b*b= b^6

Answer 9

One more going off of what you said earlier, if we had one like this \[(\frac{ 27x^2z }{ -3x^2z^6 }\]

Answer 10

And we want to know what z is

Answer 11

Then I have simplified this (probably incorrectly) to -9z^-5

Answer 12

that looks good.

x^2/x^2 is 1 (goes away)
27/-3 is -9
z/z^6 is 1/z^5 or z^-5
so \( -9 z^{-5} \) or \(-\frac{9}{z^5}\)
are correct

Answer 13

Woah I got it correct O.O thanks dude!