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anonymous

  • one year ago

how do you simplify....

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  1. anonymous
    • one year ago
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    \[(^{4}\sqrt{7^{9})}\]

  2. anonymous
    • one year ago
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    \[(^{5\sqrt{7^{3 )}}}\]

  3. UsukiDoll
    • one year ago
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    any attempts?

  4. anonymous
    • one year ago
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    into exponents?

  5. UsukiDoll
    • one year ago
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    let's start on the first problem.. that the fourth root of 7^9 right?

  6. UsukiDoll
    • one year ago
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    \[(^{4}\sqrt{7^{9})} \]

  7. anonymous
    • one year ago
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    yes s

  8. UsukiDoll
    • one year ago
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    umm let's see we need to simplify...

  9. UsukiDoll
    • one year ago
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    I'm wondering if the exponent rule can work \[x^{a}x^{b} \rightarrow x^{a+b}\]

  10. UsukiDoll
    • one year ago
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    only for that 7 though.

  11. UsukiDoll
    • one year ago
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    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
    • one year ago
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    \[\Large 7^{4}7^{b} \rightarrow 7^{4+b}\]

  13. UsukiDoll
    • one year ago
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    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
    • one year ago
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    \[\large (^{4}\sqrt{7^{8}7^{1})}\]

  15. UsukiDoll
    • one year ago
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    so rewriting this briefly in exponential form \[\LARGE 7^{\frac{8}{4}}7^{\frac{1}{4}}\]

  16. UsukiDoll
    • one year ago
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    @leejee what is 8/4 ?

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