## anonymous one year ago how do you simplify....

1. anonymous

$(^{4}\sqrt{7^{9})}$

2. anonymous

$(^{5\sqrt{7^{3 )}}}$

3. UsukiDoll

any attempts?

4. anonymous

into exponents?

5. UsukiDoll

let's start on the first problem.. that the fourth root of 7^9 right?

6. UsukiDoll

$(^{4}\sqrt{7^{9})}$

7. anonymous

yes s

8. UsukiDoll

umm let's see we need to simplify...

9. UsukiDoll

I'm wondering if the exponent rule can work $x^{a}x^{b} \rightarrow x^{a+b}$

10. UsukiDoll

only for that 7 though.

11. UsukiDoll

and we need the fourth root.. we have 7^9, but we need a fourth root... we can split this up if the 4th root is required .. We need anything to the fourth power.. so I let x = 7 and a =4. If the total exponent is 9 who is going to be my b? it's like solving a +b = 9 (for the exponent portion) 4+b=9

12. UsukiDoll

$\Large 7^{4}7^{b} \rightarrow 7^{4+b}$

13. UsukiDoll

wait.. it turns out that there is more than 1 7^4 I'm going to use the exponent rule again $\large 7^{8+1} \rightarrow 7^{8}7^1$

14. UsukiDoll

$\large (^{4}\sqrt{7^{8}7^{1})}$

15. UsukiDoll

so rewriting this briefly in exponential form $\LARGE 7^{\frac{8}{4}}7^{\frac{1}{4}}$

16. UsukiDoll

@leejee what is 8/4 ?