## anonymous one year ago FAN, FAN TESTIMONIAL, AND MEDAL!!! PLEASE HELP! Rewrite the rational exponent as a radical expression. 3 to the 2 over 3 power, to the 1 over 6 power the sixth root of 3 the ninth root of 3 the eighteenth root of 3 the sixth root of 3 to the third power I know it's not A.

1. BTaylor

So it looks like this? $\frac{ 3^2 }{ 3^{1/6} }$

2. BTaylor

or this? $\left(3^{2/3}\right)^{1/6}$

3. anonymous

Which option is it?

4. BTaylor

I'm pretty sure the problem is asking about the second one, but it isn't very clear. When you have a number to an exponent, and that quantity to another power, you multiply the two exponents. So, $$\frac{2}{3} \times \frac{1}{6}$$

5. anonymous

1/9

6. BTaylor

Exactly. So, that is the ninth root of 3.

7. anonymous

8. BTaylor

sure

9. anonymous

Explain how the Quotient of Powers was used to simplify this expression. 5 to the fourth power, over 25 = 52 By simplifying 25 to 52 to make both powers base five, and subtracting the exponents By simplifying 25 to 52 to make both powers base five, and adding the exponents By finding the quotient of the bases to be, one fifth and cancelling common factors By finding the quotient of the bases to be, one fifthand simplifying the expression

10. BTaylor

The first option is correct. $$5^4/5^2 = 5^{4-2} = 5^2 = 25$$

11. anonymous

Thanks! Sorry, but could you help me with a couple more?

12. anonymous

Rewrite the rational exponent as a radical by extending the properties of integer exponents. 2 to the 3 over 4 power, all over 2 to the 1 over 2 power the eighth root of 2 to the third power the square root of 2 to the 3 over 4 power the fourth root of 2 the square root of 2

13. anonymous

@hahagotem plz help i'll fan you too

14. BTaylor

Since these two exponents are divided, you have $$2^{3/4 - 1/2}$$.

15. anonymous

1/4?

16. BTaylor

Yes, you get $$2^{1/4}$$. When you have a number to a fractional exponent, it is a root. So, $$2^{1/4}$$ is the fourth root of 2.

17. anonymous

So C?

18. BTaylor

yes

19. anonymous

I have 1 more can u plz help?

20. BTaylor

absolutely.

21. anonymous

A rectangle has a length of the fifth root of 16 inches and a width of 2 to the 1 over 5 power inches. Find the area of the rectangle. 2 to the 3 over 5 power inches squared 2 to the 4 over 5 power inches squared 2 inches squared 2 to the 2 over 5 power inches squared

22. anonymous

I'm sorry to rush, but I have to get off soon

23. anonymous

Thanks!

24. BTaylor

@Jacob902 is correct. $$2^{4/5} \times 2^{1/5} = 2$$

25. Jacob902

why ?

26. BTaylor

$$16 = 2^4$$, so the fifth root of 16 is $$2^{4/5}$$. When you multiply two exponents with the same base, you add the two powers together. $$2^1 = 2$$.