Question

What is the simplified form of the following expression?

Answer 1

\[\frac{ \frac{ x }{ y^5 } }{ \frac{ x^2 }{ y^2 } }\]

Answer 2

@ganeshie8

Answer 3

\(\bf \large { \cfrac{ \frac{ x }{ y^5 } }{ \frac{ x^2 }{ y^2 }} \\ \quad \\
\textit{recall that}\quad \cfrac{\quad \frac{a}{b}\quad }{\frac{c}{d}}\implies \cfrac{a}{b}\cdot \cfrac{d}{c}\qquad thus\\ \quad \\
\cfrac{ \frac{ x }{ y^5 } }{ \frac{ x^2 }{ y^2 }}\implies \cfrac{ x }{ y^5 }\cdot \cfrac{ y^2 }{ x^2 }}\)

Answer 4

so it's x^3y^7?

Answer 5

oh wait.... would I simplify it?

Answer 6

yes, you can simplify it

Answer 7

I got xy^2 but that isn't one of the answers on my worksheet... It's multiple choice

Answer 8

@jdoe0001

Answer 9

\(\bf \cfrac{ \frac{ x }{ y^5 } }{ \frac{ x^2 }{ y^2 }}\implies \cfrac{ x }{ y^5 }\cdot \cfrac{ y^2 }{ x^2 }\implies \cfrac{xy^2}{y^5x^2}\)

see any factors you can cancel out?

Answer 10

when I combined the like terms the first time, I got \[\frac{ x^3y^7 }{ x^2y^5 }\] then when I simplify it, I get xy^2.... That isn't one of the choices though

Answer 11

\(\bf \large { \cfrac{ \frac{ x }{ y^5 } }{ \frac{ x^2 }{ y^2 }} \\ \quad \\
\textit{recall that}\quad \color{red}{\cfrac{\quad \frac{a}{b}\quad }{\frac{c}{d}}\implies \cfrac{a}{b}\cdot \cfrac{d}{c}}\qquad thus\\ \quad \\
\cfrac{ \frac{ x }{ y^5 } }{ \frac{ x^2 }{ y^2 }}\implies \cfrac{ x }{ y^5 }\cdot \cfrac{ y^2 }{ x^2 }}\)

Answer 12

and then you have to get a common denominator... the Common denominator would be x^2y^5 then you'd multiply the x by x^2 and the y^2 by y^5 thus getting x^3y^7/x^2y^5...... Right?

Answer 13

hmmm are you using Internet Explorer by any chance?

Answer 14

@jdoe0001

Answer 15

no..... why?

Answer 16

hmm well... ahemm... do you see how to do a fraction of fractions?

Answer 17

\(\huge \color{red}{\cfrac{\quad \frac{a}{b}\quad }{\frac{c}{d}}\implies \cfrac{a}{b}\cdot \cfrac{d}{c}}\)

Answer 18

yes

Answer 19

\(\huge \cfrac{ \frac{ x }{ y^5 } }{ \frac{ x^2 }{ y^2 }}\implies \cfrac{ x }{ y^5 }\cdot \cfrac{ y^2 }{ x^2 }\implies \cfrac{xy^2}{y^5x^2}\)

Answer 20

so it's xy^3?

Answer 21

\(\bf \Large \cfrac{xy^2}{y^5x^2}\implies \cfrac{\color{blue}{x}\color{green}{yy}}{\color{green}{yy}yyy\color{blue}{x}x}\)

see any terms to cancel out?

Answer 22

you're correct.... just don't forget is just the denominator, so \(\bf \cfrac{xy^2}{y^5x^2}\implies \cfrac{1}{y^3x}\)