Question

WILL BE GIVEN A MEDAL!

How do you solve this problem? Please list steps, so I can understand how to complete such a problem.

http://imgur.com/FC1em8I

Answer 1

start by distributing the exponent in the denominator using exponent property :

\[\large (abc)^n = a^n\cdot b^n\cdot c^n\]

Answer 2

\[\large \left(2x^3y^{-7}\right)^{-2} = ?\]

Answer 3

@rational

\[2x ^{-6}y ^{14}\]

Answer 4

thats a very good try, but looks you forgot to distribute exponent to the first term : \(2\)

Answer 5

remember \(\large 2 = 2^1\)

Answer 6

Oh yes lol, it should be

1/4x^-5y^14

Answer 7

yes! step by step
leave it in negative exponents for now

Answer 8

\[\large \left(2x^3y^{-7}\right)^{-2} = 2^{-2}\cdot x^{-6}\cdot y^{14}\]

Answer 9

plug that in the denominator of given expression :
\[\large \dfrac{3x^{-4}y^5}{2^{-2}\cdot x^{-6}\cdot y^{14}}\]

Answer 10

And then cancel out common terms, yes?

Answer 11

next usually i do a small trick.. see if it makes sense :

if the exponent is negative then flip it to the opposite side and make it positive

Answer 12

\[\large \dfrac{3\color{red}{x^{-4}}y^5}{2^{-2}\cdot x^{-6}\cdot y^{14}}\]

look at numerator, here the exponent of x is negative
so simply send that down and make the exponent positve :

\[\large \dfrac{3y^5}{2^{-2}\cdot x^{-6}\cdot y^{14}\cdot \color{red}{x^{4}}}\]

Answer 13

similarly you can send the bottom terms with negative exponents to up and make the exponent positive :



\[\large \dfrac{3y^5}{2^{-2}\cdot x^{-6}\cdot y^{14}\cdot \color{red}{x^{4}}}\]

becomes

\[\large \dfrac{3y^5\cdot 2^2\cdot x^6}{y^{14}\cdot \color{red}{x^{4}}}\]

Answer 14

if that looks any easier..

Answer 15

It actually does, thank you! From there, I'm guessing I'd have to multiply and then cancel common terms?

Answer 16

@rational

Answer 17

Exactly! give it a try...