Question

how do you simplify....

Answer 1

\[(^{4}\sqrt{7^{9})}\]

Answer 2

\[(^{5\sqrt{7^{3 )}}}\]

Answer 3

any attempts?

Answer 4

into exponents?

Answer 5

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

Answer 6

\[(^{4}\sqrt{7^{9})} \]

Answer 7

yes
s

Answer 8

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

Answer 9

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

Answer 10

only for that 7 though.

Answer 11

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

Answer 12

\[\Large 7^{4}7^{b} \rightarrow 7^{4+b}\]

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

@leejee what is 8/4 ?