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anonymous

  • one year ago

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

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  1. zepdrix
    • one year ago
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    Hey King! Is this what your problem looks like?\[\large\rm \sqrt{x}\cdot\sqrt[4]{x}\]

  2. anonymous
    • one year ago
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    yes :)

  3. zepdrix
    • one year ago
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    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.

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

  5. anonymous
    • one year ago
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    would you reduce the second one to 2?

  6. zepdrix
    • one year ago
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    No.\[\LARGE\rm \sqrt[\color{orangered}{n}]{x}=x^{1/\color{orangered}{n}}\qquad\to\qquad \sqrt[\color{orangered}{4}]{x}=x^{1/\color{orangered}{4}}\]

  7. zepdrix
    • one year ago
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    \[\large\rm \sqrt[2]{x}\cdot\sqrt[4]{x}\quad=\quad x^{1/2}\cdot x^{1/4}\]

  8. zepdrix
    • one year ago
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    From here you need to apply one of your exponent rules:\[\large\rm \color{royalblue}{x^a\cdot x^b=x^{a+b}}\]

  9. anonymous
    • one year ago
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    oh yeah sorry i was confused but I see how it's 1/4

  10. anonymous
    • one year ago
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    @zepdrix is that it after that step ?

  11. zepdrix
    • one year ago
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    You need to apply the blue formula. So you would have to add 1/2 and 1/4.

  12. zepdrix
    • one year ago
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    You'll need a common denominator to add those two fractions together.

  13. anonymous
    • one year ago
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    the common denominator would be 2 right ?

  14. anonymous
    • one year ago
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    @zepdrix

  15. zepdrix
    • one year ago
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    \[\large\rm \frac{1}{2}+\frac{1}{4}\]The common denominator is 4. How do you turn the 2 into a 4?

  16. anonymous
    • one year ago
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    multiplying it by 2

  17. zepdrix
    • one year ago
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    \[\large\rm \color{royalblue}{\frac{2}{2}}\cdot\frac{1}{2}+\frac{1}{4}\quad=\quad \frac{2}{4}+\frac{1}{4}\]Good good good.

  18. anonymous
    • one year ago
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    wait when you said I had to apply one of the exponent rules what was it called?

  19. zepdrix
    • one year ago
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    It was the one that I colored in blue. I think it's called the Exponent Addition Rule

  20. zepdrix
    • one year ago
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    something like that

  21. anonymous
    • one year ago
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    the final answer simplified and all would be x^3/4 or am I wrong ? @zepdrix

  22. zepdrix
    • one year ago
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    yay good job \c:/

  23. anonymous
    • one year ago
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    thank you for the help. it was much needed

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