Here's the question you clicked on:
poopsiedoodle
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
So, I need them in radical form.
Factor everything first and then apply your radical rules... for example \[\sqrt[3]{x^3} = x\]
Problem is that I have no idea what you're saying. ._.
Ok for example \[\sqrt[8]{256x^4}\] becomes, if you factor \[\sqrt[8]{2^{8}x^4}\] which then becomes \[2\sqrt[8]{x^4}=2 x^{\frac{4}{8}}=2x^{1/2}=2\sqrt{2}\]
This uses the idea that \[\sqrt[a]{x} = x^{1/a}\]
just 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.
the ^ means exponents. like, 2^3 is 2 cubed.
\(\Large\text{But again, I have no idea how to do this.}\)
is ^3v/56x^14 supposed to be \[\bigg(\sqrt{56x^{14}}\bigg)^3\] then?
So, \(\huge\sqrt[8]{256x^4}\) 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? \(\huge\text{:|}\)
Sorry that should be \[2\sqrt{x}\]
and no, it's supposed to be \[^{3}\sqrt{56x^{14}}\]
ok the basic theorems that you need for these type of problems are that \[\sqrt[a]{x} = x^{\frac{1}{a}}\] So for example \[\large \sqrt[3]{x^{10}}\to x^{\frac{10}{3}}\to x^3x^{\frac{1}{3}}\to x^3\sqrt[3]{x}\]
I understand the first half of your example equation, but not the second half.
So 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 \[7^{1/3}2x^{4}x^{2/3}\to 2x^4 7^{1/3}x^{1/3}\to 2x^4\sqrt[3]{7x}\]
my brain is about to explode. e_o
So 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 \[x^{9/3 + 1/3}\to x^{9/3}x^{1/3}\to x^3x^{1/3}\]
again, might I suggest the larger font size? Maybe Large would be a good replacement for huge though.