how do you simplify....

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how do you simplify....

Mathematics
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\[(^{4}\sqrt{7^{9})}\]
\[(^{5\sqrt{7^{3 )}}}\]
any attempts?

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into exponents?
let's start on the first problem.. that the fourth root of 7^9 right?
\[(^{4}\sqrt{7^{9})} \]
yes s
umm let's see we need to simplify...
I'm wondering if the exponent rule can work \[x^{a}x^{b} \rightarrow x^{a+b}\]
only for that 7 though.
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
\[\Large 7^{4}7^{b} \rightarrow 7^{4+b}\]
wait.. it turns out that there is more than 1 7^4 I'm going to use the exponent rule again \[\large 7^{8+1} \rightarrow 7^{8}7^1\]
\[\large (^{4}\sqrt{7^{8}7^{1})}\]
so rewriting this briefly in exponential form \[\LARGE 7^{\frac{8}{4}}7^{\frac{1}{4}}\]
@leejee what is 8/4 ?

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