anonymous
  • anonymous
my question.......
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\sqrt[4]{486x ^{12}y ^{14}}\] simplify
anonymous
  • anonymous
would it be \[3x ^{3}y ^{3}\] on the oustide and then \[\sqrt[4]{6y ^{2}}\]
anonymous
  • anonymous
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anonymous
  • anonymous
anyone could help my assignment please
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anonymous
  • anonymous
The first thing you should do is try to break 486 down into prime factors and put some into powers of 4. So, \[486=2 \times 3^5\]factored into primes. Now, we can write,\[486=2 \times 3 \times 3^4=6\times 3^4\]Now we can write,\[(6 \times 3^4x^{12}y^{14})^{1/4}=6^{1/4}\times (3^4)^{1/4}\times (x^{12})^{1/4}\times (y^{14})^{1/4}\]\[=\sqrt[4]{6} \times 3^{4/4} \times x^{12/4} \times y ^{14/4}\]\[=\sqrt[4]{6}\times3\times x^3 \times y^{7/2}\]\[=3\sqrt[4]{6}x^3y^{7/2}\]

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