anonymous
  • anonymous
Rewrite in simplest rational exponent form √x • 4√x. Please show each step of your process
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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zepdrix
  • zepdrix
Hey King! Is this what your problem looks like?\[\large\rm \sqrt{x}\cdot\sqrt[4]{x}\]
anonymous
  • anonymous
yes :)
zepdrix
  • zepdrix
When 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.

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zepdrix
  • zepdrix
\[\large\rm \sqrt[2]{x}\cdot\sqrt[4]{x}\quad=\quad x^{1/2}\cdot \text{__}\] So that's a way I could rewrite my first radical. How bout the other one? :) Any ideas?
anonymous
  • anonymous
would you reduce the second one to 2?
zepdrix
  • zepdrix
No.\[\LARGE\rm \sqrt[\color{orangered}{n}]{x}=x^{1/\color{orangered}{n}}\qquad\to\qquad \sqrt[\color{orangered}{4}]{x}=x^{1/\color{orangered}{4}}\]
zepdrix
  • zepdrix
\[\large\rm \sqrt[2]{x}\cdot\sqrt[4]{x}\quad=\quad x^{1/2}\cdot x^{1/4}\]
zepdrix
  • zepdrix
From here you need to apply one of your exponent rules:\[\large\rm \color{royalblue}{x^a\cdot x^b=x^{a+b}}\]
anonymous
  • anonymous
oh yeah sorry i was confused but I see how it's 1/4
anonymous
  • anonymous
@zepdrix is that it after that step ?
zepdrix
  • zepdrix
You need to apply the blue formula. So you would have to add 1/2 and 1/4.
zepdrix
  • zepdrix
You'll need a common denominator to add those two fractions together.
anonymous
  • anonymous
the common denominator would be 2 right ?
anonymous
  • anonymous
@zepdrix
zepdrix
  • zepdrix
\[\large\rm \frac{1}{2}+\frac{1}{4}\]The common denominator is 4. How do you turn the 2 into a 4?
anonymous
  • anonymous
multiplying it by 2
zepdrix
  • zepdrix
\[\large\rm \color{royalblue}{\frac{2}{2}}\cdot\frac{1}{2}+\frac{1}{4}\quad=\quad \frac{2}{4}+\frac{1}{4}\]Good good good.
anonymous
  • anonymous
wait when you said I had to apply one of the exponent rules what was it called?
zepdrix
  • zepdrix
It was the one that I colored in blue. I think it's called the Exponent Addition Rule
zepdrix
  • zepdrix
something like that
anonymous
  • anonymous
the final answer simplified and all would be x^3/4 or am I wrong ? @zepdrix
zepdrix
  • zepdrix
yay good job \c:/
anonymous
  • anonymous
thank you for the help. it was much needed

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