## anonymous 3 years ago What is the product in simplest form? State any restrictions on the variable.

1. anonymous

(4a^5/7b^4) * (2b^2/2a^4)

2. anonymous

@Hero

3. Hero

Rewrite like this: $\frac{4a^5 \dot\ 2b^2}{2a^4 \dot\ 7b^4}$

4. anonymous

ok and then?

5. anonymous

do i just multiply accross?

6. Hero

Or you can work with each separately by re-writing like this: $\frac{4}{2} \dot\ \frac{a^5}{a^4} \dot\ \frac{2}{7} \dot\ \frac{b^2}{b^4}$

7. anonymous

so it would be 8ab^7??

8. anonymous

for the top part?

9. Hero

No

10. anonymous

wow thats confusing o.O

11. Hero

You already know how to reduce the numerical fractions.

12. Hero

You know that 4/2 = 2. You also know that 2/7 is already in simplest form and cannot be reduced any further

13. anonymous

mhk

14. Hero

So for the numbers, you are just left with $2 \times \frac{2}{7} = \frac{4}{7}$

15. Hero

For the variables, you have to use this rule: $\frac{a^y}{a^x} = a^{y - x}, y > x$ $\frac{b^x}{b^y} = \frac{1}{b^{y-x}}, x<y$

16. Hero

So $\frac{a^5}{a^4} = a^{5 - 4} = a^1 = a$ $\frac{b^2}{b^4} = \frac{1}{b^{4-2}} = \frac{1}{b^2}$

17. anonymous

thes are my multiple choice answers: 4a^9/7b^^6 4a/7b^2 7b^2/4a 4/7a^9b^6

18. Hero

$\frac{4}{7} \times a \times \frac{1}{b^2} = \frac{4a}{7b^2}$

19. anonymous

alirght so B? Thanks! <3

20. Hero

You should learn how to do these on your own.