Question

Please help! Will give both fan and medal :)

Divide and simplify.
7 sqrt 14x^6 / 7 sqrt 2x^5

Thank you in advance!

Answer 1

Is it this?
\[\Large \frac{7\sqrt{14x^6}}{7\sqrt{2x^5}}\]
or is it this
\[\Large \frac{\sqrt[7]{14x^6}}{\sqrt[7]{2x^5}}\]

Answer 2

The first :) @jim_thompson5910

Answer 3

ok so the first thing we do is we can cancel out the 7s

since 7 over 7 = 1

\[\Large \frac{7\sqrt{14x^6}}{7\sqrt{2x^5}}\]

\[\Large \frac{\color{red}{7}\sqrt{14x^6}}{\color{red}{7}\sqrt{2x^5}}\]

\[\Large \frac{\color{red}{\cancel{7}}\sqrt{14x^6}}{\color{red}{\cancel{7}}\sqrt{2x^5}}\]

\[\Large \frac{\sqrt{14x^6}}{\sqrt{2x^5}}\]

agreed?

Answer 4

Agreed

Answer 5

then we use the rule

\[\Large \frac{\sqrt{x}}{\sqrt{y}} = \sqrt{\frac{x}{y}}\]

to get

\[\Large \frac{\sqrt{14x^6}}{\sqrt{2x^5}}=\sqrt{\frac{14x^6}{2x^5}}\]

what comes next?

Answer 6

sorry

Answer 7

this is a step by step sort of a thing

Answer 8

Divide?

Answer 9

You're fine! @Houdini_Dragon yes, it is :)

Answer 10

yes, you need to simplify \(\LARGE \frac{14x^6}{2x^5}\)

Answer 11

Sorry! My internet messed up. Is it, 7x^11?

Answer 12

when you divide variables like that, you SUBTRACT the exponents

Answer 13

Rule:
\[\LARGE \frac{x^a}{x^b} = x^{a-b}\]

Answer 14

Example

\[\LARGE \frac{x^9}{x^4} = x^{9-4}=x^5\]

Answer 15

`Is it, 7x^11?` close but not quite 100% correct

Answer 16

7x^-1 ?

Answer 17

@jim_thompson5910 :)

Answer 18

the exponent up top is 6
the exponent in the bottom is 5

(top exponent) - (bottom exponent) = 6-5 = 1

so 1 is the final exponent

Answer 19

\[\LARGE \frac{x^6}{x^5} = x^{6-5}=x^1 = x\]

Answer 20

Yeh, I noticed I made that mistake, I meant positive 1, not negative.

Answer 21

So all this means
\[\Large \sqrt{\frac{14x^6}{2x^5}} = \sqrt{7x}\]

Answer 22

Ahh, I see. And that's our final answer, correct?

Answer 23

correct

Answer 24

Okay. Thank you very much :)

Answer 25

\[\Large \frac{7\sqrt{14x^6}}{7\sqrt{2x^5}}=\sqrt{7x}\]

Answer 26

np