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REY [17]
2 years ago
13

What is the simplified form of StartRoot StartFraction 72 x Superscript 16 Baseline Over 50 x Superscript 36 Baseline EndFractio

n EndRoot? Assume x ≠ 0.
StartFraction 6 Over 5 x Superscript 10 Baseline EndFraction
StartFraction 6 Over 5 x squared EndFraction
Six-fifths x Superscript 10
Six-fifths x squared
Mark this and return
Mathematics
1 answer:
aalyn [17]2 years ago
9 0

Answer:

  StartFraction 6 Over 5 x Superscript 10 Baseline EndFraction

Step-by-step explanation:

Apparently you want to simplify ...

  \sqrt{\dfrac{72x^{16}}{50x^{36}}}

The applicable rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  1/a^b = a^-b

  (a^b)^c = a^(bc)

__

So the expression simplifies as ...

  \sqrt{\dfrac{72x^{16}}{50x^{36}}}=\sqrt{\dfrac{36}{25x^{36-16}}}=\sqrt{\dfrac{36}{25x^{20}}}\\\\\sqrt{\left(\dfrac{6}{5x^{10}}\right)^2}=\boxed{\dfrac{6}{5x^{10}}}

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