Question

Can someone explain this to me?

Answer 1

Simplify the following expression. Express the answer w/positive exponents

(3xy^-1/y^3) ^-4

Answer 2

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

(3x/y^2) ^-4 = (3x)^-4/(y^2)^-4 = 3^-4 x^-4/y^-8

= y^8/81x^4

Answer 3

I know that my answer is wrong.. Where did I mess up?

Answer 4

it's not clear what the starting expression is.
\[ \left(\frac{3xy^{-1}}{y^3}\right)^{-4} \]?

Answer 5

Yes thats correct.. Sorry I dont get how to use the equation thing.

Answer 6

ok so the y's inside the parens can be handled a few ways. one way:
write y^-1 as 1/y
\[ \left(\frac{3x}{y \cdot y^3}\right)^{-4} \\
\]

Answer 7

the other way: y^-1 / y^3 . keep the base y. new exponent is top minus bottom exponents: -1 - 3 = -4. so y^-4
\[ \left(3xy^{-4}\right)^{-4} \\
=\left(\frac{3x}{y^4}\right)^{-4} \\\]

Answer 8

I would "flip" the fraction and change the sign of the -4 exponent to +4
\[ \left(\frac{y^4}{3x}\right)^{4} \]

Answer 9

can you finish ?

Answer 10

Um I think so... Give me a second

Answer 11

I have

y^-16/ 3^4 x^-4 = y^-16/?

Answer 12

I know the final answer is y^16/(3x)^4 but im stuck on the last part

Answer 13

if you start with
\[ \left(\frac{y^4}{3x}\right)^{4} \]
all the exponents stay positive

Answer 14

if we do it "brute force"
remember that
\[ \left(\frac{y^4}{3x}\right)^{4} = \left(\frac{y^4}{3x}\right) \left(\frac{y^4}{3x}\right) \left(\frac{y^4}{3x}\right) \left(\frac{y^4}{3x}\right)\]

Answer 15

and when you multiply fractions, you multiply top times top
y^4 * y^4 * y^4 *y^4 = y^16
(the short way is to use the rule
\[ (a^b)^c= a^{b\cdot c} \]

Answer 16

and the bottom is
\[ \left( 3x\right)^4 \]

Answer 17

or 3^4 * x^4
or
81x^4

there are a few ways to write it.

Answer 18

Alright thank you!

Answer 19

btw, when you started
***
Simplify the following expression. Express the answer w/positive exponents
(3xy^-1/y^3) ^-4
****
on the next post you say
= (3x/ y^-1 y^3) ^-4 = (3x/y^2) ^-4

notice you changed 3xy^-1 to 3x/y^-1
when you do that (move y^-1 from the "top" to the "bottom"), you should change the sign of the exponent. you should have written:
= (3x/ y^1 y^3) ^-4
and then you get
= (3x/y^4) ^-4
and now you will get the correct answer

Answer 20

I see

Answer 21

and to complete the thought... the other way to do this
is
\[ \left(\frac{y^4}{3x}\right)^{4}= \frac{\left( y^4\right)^4}{\left( 3x\right)^4}\]
and then simplify the top using the rule
\[ (a^b)^c= a^{bc} \]
to get \(y^{4\cdot 4} = y^{16}\)