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 2 years ago
For problems 1–5, simplify the expression. Answers written in decimal form will not be accepted. Each of these problems is worth 1 point.
"v/" is a radical by the way
___
1.v/96
______
2. 8 v/63x^5
___________
3. v/128x^5y^2
___
4. ^3v/32
________
5. ^3v/56x^14
 2 years ago
For problems 1–5, simplify the expression. Answers written in decimal form will not be accepted. Each of these problems is worth 1 point. "v/" is a radical by the way ___ 1.v/96 ______ 2. 8 v/63x^5 ___________ 3. v/128x^5y^2 ___ 4. ^3v/32 ________ 5. ^3v/56x^14

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poopsiedoodle
 2 years ago
Best ResponseYou've already chosen the best response.1So, I need them in radical form.

freewilly922
 2 years ago
Best ResponseYou've already chosen the best response.1Factor everything first and then apply your radical rules... for example \[\sqrt[3]{x^3} = x\]

poopsiedoodle
 2 years ago
Best ResponseYou've already chosen the best response.1Problem is that I have no idea what you're saying. ._.

freewilly922
 2 years ago
Best ResponseYou've already chosen the best response.1Ok for example \[\sqrt[8]{256x^4}\] becomes, if you factor \[\sqrt[8]{2^{8}x^4}\] which then becomes \[2\sqrt[8]{x^4}=2 x^{\frac{4}{8}}=2x^{1/2}=2\sqrt{2}\]

freewilly922
 2 years ago
Best ResponseYou've already chosen the best response.1This uses the idea that \[\sqrt[a]{x} = x^{1/a}\]

poopsiedoodle
 2 years ago
Best ResponseYou've already chosen the best response.1just wondering, would you mind using bigger font? I can't see the exponents. To do that, put what you are saying in the curly braces in \(\huge\text{}\.) but take out the . at the end.

poopsiedoodle
 2 years ago
Best ResponseYou've already chosen the best response.1the ^ means exponents. like, 2^3 is 2 cubed.

poopsiedoodle
 2 years ago
Best ResponseYou've already chosen the best response.1\(\Large\text{But again, I have no idea how to do this.}\)

freewilly922
 2 years ago
Best ResponseYou've already chosen the best response.1is ^3v/56x^14 supposed to be \[\bigg(\sqrt{56x^{14}}\bigg)^3\] then?

poopsiedoodle
 2 years ago
Best ResponseYou've already chosen the best response.1So, \(\huge\sqrt[8]{256x^4}\) turns into \(\huge\sqrt[8]{2^{8}x^4}\) which turns into \(\huge2\sqrt[8]{x^4}=2 x^{\frac{4}{8}}=2x^{1/2}=2\sqrt{2}\) But how? \(\huge\text{:}\)

freewilly922
 2 years ago
Best ResponseYou've already chosen the best response.1Sorry that should be \[2\sqrt{x}\]

poopsiedoodle
 2 years ago
Best ResponseYou've already chosen the best response.1and no, it's supposed to be \[^{3}\sqrt{56x^{14}}\]

freewilly922
 2 years ago
Best ResponseYou've already chosen the best response.1ok the basic theorems that you need for these type of problems are that \[\sqrt[a]{x} = x^{\frac{1}{a}}\] So for example \[\large \sqrt[3]{x^{10}}\to x^{\frac{10}{3}}\to x^3x^{\frac{1}{3}}\to x^3\sqrt[3]{x}\]

poopsiedoodle
 2 years ago
Best ResponseYou've already chosen the best response.1I understand the first half of your example equation, but not the second half.

freewilly922
 2 years ago
Best ResponseYou've already chosen the best response.1So any complicated radical you are given you can convert to exponents, use the rules of exponents shamelessly and then convert back to radical. So \[\large \sqrt[3]{56x^{14}}\to \sqrt[3]{(7)(8)x^{14}}\to 7^{1/3}8^{1/3}x^{14/3}\] This then becomes \[ 7^{1/3}8^{1/3}x^{14/3}\to 7^{1/3}(2^3)^{1/3}x^{12/3}x^{2/3}\] becomes \[7^{1/3}2x^{4}x^{2/3}\to 2x^4 7^{1/3}x^{1/3}\to 2x^4\sqrt[3]{7x}\]

poopsiedoodle
 2 years ago
Best ResponseYou've already chosen the best response.1my brain is about to explode. e_o

freewilly922
 2 years ago
Best ResponseYou've already chosen the best response.1So you don't understand how \[x^{10/3} \to x^3x^{1/3}\]? This results from the fact that \[X^aX^b = X^{ab}\] and the reverse. So if you have \[x^{10/3}\] you have \[x^{9/3 + 1/3}\to x^{9/3}x^{1/3}\to x^3x^{1/3}\]

poopsiedoodle
 2 years ago
Best ResponseYou've already chosen the best response.1again, might I suggest the larger font size? Maybe Large would be a good replacement for huge though.
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