anonymous
  • anonymous
5x^(-5)=1/32
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
@ganeshie8
anonymous
  • anonymous
@pooja195
anonymous
  • anonymous
@Michele_Laino

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More answers

Crystal_Bliss
  • Crystal_Bliss
\[simplify \sqrt[5]{160}\to 2\sqrt[5]{5}\]
Michele_Laino
  • Michele_Laino
hint: after a simplification, i can write this: \[\Large \frac{5}{{{x^5}}} = \frac{1}{{{2^5}}}\] since \(32=2^5\)
Crystal_Bliss
  • Crystal_Bliss
Switch sides\[x=2\sqrt[5]{5}\] <- your answer
Michele_Laino
  • Michele_Laino
hint: if I take the inverse of both sides, I get: \[\Large \frac{{{x^5}}}{5} = {2^5}\] now, please multiply both sides by 5, what do you get?
anonymous
  • anonymous
idk... i was never taught exponents
anonymous
  • anonymous
@Michele_Laino ????
Michele_Laino
  • Michele_Laino
after the indicated multiplication, I get: \[\huge {x^5} = 5 \cdot {2^5}\] then I have to make the \(5-th\) rooth of both sides, so I can write: \[\huge \sqrt[5]{{{x^5}}} = \sqrt[5]{5} \cdot \sqrt[5]{{{2^5}}}\] now, please apply this rule to both sides: \[\huge \sqrt[5]{{{a^m}}} = {a^{\frac{m}{5}}}\] what do you get?
anonymous
  • anonymous
i still have no idea, i was never taught this stuff.
Michele_Laino
  • Michele_Laino
in particular, if \(m=5\), we can write this \[\huge \begin{gathered} \sqrt[5]{{{x^5}}} = {x^{\frac{5}{5}}} = {x^1} = x \hfill \\ \hfill \\ \sqrt[5]{{{2^5}}} = {2^{\frac{5}{5}}} = {2^1} = 2 \hfill \\ \end{gathered} \]
anonymous
  • anonymous
OMG! it all just worked out in my head. one question tho, why would m=5?
Michele_Laino
  • Michele_Laino
since I wrote a more general formula, and in order to solve your exercise, we need to replace \(m=5\)
anonymous
  • anonymous
ohhh okay. thank you SOOOO much!!
Michele_Laino
  • Michele_Laino
:)

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