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

1. zepdrix

Hey King! Is this what your problem looks like?$\large\rm \sqrt{x}\cdot\sqrt[4]{x}$

2. anonymous

yes :)

3. 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.

4. 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?

5. anonymous

would you reduce the second one to 2?

6. zepdrix

No.$\LARGE\rm \sqrt[\color{orangered}{n}]{x}=x^{1/\color{orangered}{n}}\qquad\to\qquad \sqrt[\color{orangered}{4}]{x}=x^{1/\color{orangered}{4}}$

7. zepdrix

$\large\rm \sqrt[2]{x}\cdot\sqrt[4]{x}\quad=\quad x^{1/2}\cdot x^{1/4}$

8. zepdrix

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

oh yeah sorry i was confused but I see how it's 1/4

10. anonymous

@zepdrix is that it after that step ?

11. zepdrix

You need to apply the blue formula. So you would have to add 1/2 and 1/4.

12. zepdrix

You'll need a common denominator to add those two fractions together.

13. anonymous

the common denominator would be 2 right ?

14. anonymous

@zepdrix

15. zepdrix

$\large\rm \frac{1}{2}+\frac{1}{4}$The common denominator is 4. How do you turn the 2 into a 4?

16. anonymous

multiplying it by 2

17. 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.

18. anonymous

wait when you said I had to apply one of the exponent rules what was it called?

19. zepdrix

It was the one that I colored in blue. I think it's called the Exponent Addition Rule

20. zepdrix

something like that

21. anonymous

the final answer simplified and all would be x^3/4 or am I wrong ? @zepdrix

22. zepdrix

yay good job \c:/

23. anonymous

thank you for the help. it was much needed