Question

Can someone please help me? I really need help... I will fan and Medal
Question~
Simplify the following exponential expressions.

5x^6y^4
---------
-20xy^-2z

Answer 1

@phi would you mind helping me?

Answer 2

let's hope OS behaves.

meanwhile, what is 5/-20 ?
(remember this is plus divided by minus, so the answer is going to be negative)

Answer 3

-1/4

Answer 4

0?

Answer 5

oh! I meant anything divided by itself is 1!

Answer 6

oh okay, haha that's what I thought it was supposed to be! ok so x/x=1

Answer 7

all of these problems use that idea (but there are short-cuts)
if you see
\[ \frac{x}{x}\]
that is 1
if you see
\[ \frac{x\cdot x \cdot x}{x} \]
that is the same as
\[ \frac{x}{x} \cdot x\cdot x \]
and x/x is 1, so you get
\[ 1\cdot x \cdot x\]
and we can ignore multiply by 1 (it does not "do anything")
in other words you get
\[ x \cdot x\]
does that make sense?

Answer 8

you have in your problem
\[ \frac{x^6}{x} \]
the "little 6" means x times itself 6 times
so (if we wanted) we could write this as
\[ \frac{x \cdot x \cdot x \cdot x \cdot x \cdot x}{x}\]
and the x in the bottom will "cancel out" one of the x's up top
that will leave only 5 x's up top
we would write that in "short-hand" as
\[ x^5\]

Answer 9

next we do the y's
\[ \frac{y^4}{y^{-2}} \]

the bottom y is y^-2
the negative number -2 is a bit tricky. You have to learn this rule:
if you move a number or letter from bottom to top, you change the sign of the exponent

in other words, to make that -2 turn into a +2, we "move" the y^-2 up top
\[ \frac{y^4 y^2}{1} \]

that is 4 y's multiplied together times 2 more y's
so y*y*y*y * y*y
how many y's is that altogether ?

Answer 10

y=6

Answer 11

yes, but not y=6
you have
y*y*y*y*y*y
and if you don't like to write that out, just write y and put an ^ and a 6 next to it
y^6
(or if you use the equation editor, or write it) make the 6 small in the upper right.
\[ y^6\]

Answer 12

do you understand how the "short-cut" way to write it works ?

Answer 13

yes sir

Answer 14

do you know how to write
x*x*x*x

using the short way ?

Answer 15

x^4?

Answer 16

yes.

and do you know how to write
y^3
the "long way" ?

Answer 17

y*y*y
do you mean this way?

Answer 18

yes.

you are doing good.

now can you simplify
\[ \frac{x\cdot x\cdot x}{x\cdot x\cdot x} \]
notice you can "cancel" each "pair of x" (one in the top with one in the bottom)

Answer 19

yes sir

Answer 20

what does it simplify to ?

Answer 21

@phi it equals 0?

Answer 22

\[ \frac{x\cdot x\cdot x}{x\cdot x\cdot x} \\= \frac{x}{x}\cdot\frac{x}{x}\cdot\frac{x}{x} \\ = 1\cdot 1\cdot 1\\=1
\]