what is the simplified form of sqaure root 72x to the power 16 over 50x 36 assume x = 0 1)6 over 5x power of 10 2)6 over 5x to po

Question

what is the simplified form of sqaure root 72x to the power 16 over 50x 36 assume x = 0
1)6 over 5x power of 10
2)6 over 5x to power of 2
3)6 over 5x to the power of 10
4)6 over 5x to the power of 2​

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Hailey 2 weeks 2021-09-10T12:38:30+00:00 1 Answer 0

Answers ( )

    0
    2021-09-10T12:39:31+00:00

    Answer:

    \large\boxed{\dfrac{6}{5x^{10}}}

    Step-by-step explanation:

    \sqrt{\dfrac{72x^{16}}{50x^{36}}}\qquad\text{simplify}\\\\=\sqrt{\dfrac{36x^{16}}{25x{^{20+16}}}}\qquad\text{use}\ (a^n)(a^m)=a^{n+m}\\\\=\sqrt{\dfrac{36x^{16}}{25x^{20}x^{16}}}\qquad\text{cancel}\ x^{16}\\\\=\sqrt{\dfrac{36}{25x^{20}}}\qquad\text{use}\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\ \text{and}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\dfrac{\sqrt{36}}{\sqrt{25}\cdot\sqrt{x^{10\cdot2}}}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\dfrac{6}{5\sqrt{(x^{10})^2}}\qquad\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=\dfrac{6}{5x^{10}}

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