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anonymous
 one year ago
Rewrite in simplest rational exponent form √x • 4√x. Please show each step of your process
anonymous
 one year ago
Rewrite in simplest rational exponent form √x • 4√x. Please show each step of your process

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zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Hey King! Is this what your problem looks like?\[\large\rm \sqrt{x}\cdot\sqrt[4]{x}\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1When no number is written over the radical, it's implied that it's a 2.\[\large\rm \sqrt[2]{x}\cdot\sqrt[4]{x}\]Square root = second root. Ok so in general,\[\large\rm \sqrt[n]{x}=x^{1/n}\]We can rewrite our root as a rational exponent like this. We get a fraction as an exponent. The `denominator` is the degree of the root.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm \sqrt[2]{x}\cdot\sqrt[4]{x}\quad=\quad x^{1/2}\cdot \text{__}\] So that's a way I could rewrite my first radical. How bout the other one? :) Any ideas?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would you reduce the second one to 2?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1No.\[\LARGE\rm \sqrt[\color{orangered}{n}]{x}=x^{1/\color{orangered}{n}}\qquad\to\qquad \sqrt[\color{orangered}{4}]{x}=x^{1/\color{orangered}{4}}\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm \sqrt[2]{x}\cdot\sqrt[4]{x}\quad=\quad x^{1/2}\cdot x^{1/4}\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1From here you need to apply one of your exponent rules:\[\large\rm \color{royalblue}{x^a\cdot x^b=x^{a+b}}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh yeah sorry i was confused but I see how it's 1/4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@zepdrix is that it after that step ?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1You need to apply the blue formula. So you would have to add 1/2 and 1/4.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1You'll need a common denominator to add those two fractions together.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the common denominator would be 2 right ?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm \frac{1}{2}+\frac{1}{4}\]The common denominator is 4. How do you turn the 2 into a 4?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm \color{royalblue}{\frac{2}{2}}\cdot\frac{1}{2}+\frac{1}{4}\quad=\quad \frac{2}{4}+\frac{1}{4}\]Good good good.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wait when you said I had to apply one of the exponent rules what was it called?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1It was the one that I colored in blue. I think it's called the Exponent Addition Rule

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the final answer simplified and all would be x^3/4 or am I wrong ? @zepdrix

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank you for the help. it was much needed
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