## chrisGA one year ago Evaluate fourth root of 9 multiplied by square root of 9 over the fourth root of 9 to the power of 5.

1. chrisGA

9 to the power of negative 1 over 2 9 to the power of negative 1 over 4 9 92

2. anonymous

If I understand correctly, the question is to simplify$\frac{ 9^{\frac{ 1 }{ 4 }} \times 9^{\frac{ 1 }{ 2 }} }{ \left( 9^{\frac{ 1 }{ 4 }} \right)^{5} }$Is this correct?

3. chrisGA

4. anonymous

OK. When working with exponents, many times it is easier to express them as fractions rather than radicals. My statement is equivalent to yours. Do you understand the fractional exponents?

5. chrisGA

yes a lil

6. anonymous

For example,$\sqrt{x}=x ^{\frac{ 1 }{ 2 }}$$\sqrt[3]{x}=x ^{\frac{ 1 }{ 3 }}$$\sqrt[4]{x}=x ^{\frac{ 1 }{ 4 }}$$\sqrt[4]{x ^{5}}=\left( x ^{5} \right)^{\frac{ 1 }{ 4 }}=x ^{\frac{ 5 }{ 4 }}$

7. anonymous

So, with the expression written with fractional exponents, simplify the numerator first. The rule when multiplying powers with the same base is to ADD the exponents. Then, divide the numerator by the denominator, The rule when dividing powers with the same base is that you SUBTRACT the exponents. This help?

8. chrisGA

it does a lil bit what would the answer be?

9. anonymous

For example,$\frac{ 3^{\frac{ 1 }{ 4 }}\times 3^{\frac{ 1 }{ 2 }} }{ 3^{\frac{ 7 }{ 4 }} }=\frac{ 3^{\frac{ 3 }{ 4 }} }{ 3^{\frac{ 7 }{ 4 }} }=3^\left( \frac{ 3 }{ 4 } -\frac{ 7 }{ 4 }\right)=3^{-\frac{ 4 }{ 4 }}=3^{-1}$

10. anonymous

Sorry for taking so long with the typing. I can't give you the answer, but I can check yours. What do you get?

11. chrisGA

it ok and i got B? is that correct

12. anonymous

Don't think so. Let's take it one step at a time. What do you get when you simplify just the numerator?

13. chrisGA

9

14. anonymous

$9^{\frac{ 1 }{ 4 }}\times 9^{\frac{ 1 }{ 2 }} = 9^{\left( \frac{ 1 }{ 4 } +\frac{ 1 }{ 2 }\right)}=?$

15. chrisGA

is it C?

16. anonymous

Don't think so. How about simplifying the numerator first, as above. What would you get?

17. anonymous

What is 1/4 + 1/2 ?

18. chrisGA

3/4

19. anonymous

Hello? Do you still want my help?

20. chrisGA

3/4

21. anonymous

Right on! So the numerator simplifies to$9^{\frac{ 3 }{ 4 }}$Now simplify the denominator. It is a power raise to another exponent. The rule in this case is to MULTIPLY the exponents. So$\left(9^{\frac{ 1 }{ 4 }} \right)^{5}=9^{?}$ What do you get?

22. chrisGA

2?

23. anonymous

No. Keep the base (9) and multiply just the exponents together.$\left( 9^{\frac{ 1 }{ 4 }} \right)^{5} = 9^{\left( \frac{ 1 }{ 4 } \times5\right)} = 9^{?}$

24. anonymous

In other words, what is 1/4 x 5 ?

25. chrisGA

5/4?

26. anonymous

Perfect. Now your problem has been simplified to $\frac{ 9^{\frac{ 3 }{ 4 }} }{ 9^{\frac{ 5 }{ 4 }} }$When dividing powers with the same base, the rule is to keep the base and SUBTRACT the exponents. Therefore$\frac{ 9^{\frac{ 3 }{ 4 }} }{ 9^{\frac{ 5 }{ 4 }} } = 9^{\left( \frac{ 3 }{ 4 } -\frac{ 5 }{ 4 }\right)} = 9^{?}$

27. anonymous

In other words, what is 3/4 - 5/4 ?

28. chrisGA

-1/2

29. anonymous

Terrific. That's your answer.$9^{-\frac{ 1 }{ 2 }}$ Lot of small step. And lots of rules for working with exponents. Well done!

30. chrisGA

thank you very much

31. anonymous

You're welcome. A bit of practice, and you'll be a master.