Question

2%20%7D%20%7D%20%7B%20%28%20%5Csqrt%20%7B%205%20%7D%20%29%20%5E%20%7B%202%20%7D%20%7D%20%5C%7D%20%5E%20%7B%20%5Cfrac%20%7B%201%20%7D%20%7B%202%20%7D%20%7D" id="TexFormula1" title="\{ \frac { ( \sqrt { 3 } ) \times 3 ^ { - 2 } } { ( \sqrt { 5 } ) ^ { 2 } } \} ^ { \frac { 1 } { 2 } }" alt="\{ \frac { ( \sqrt { 3 } ) \times 3 ^ { - 2 } } { ( \sqrt { 5 } ) ^ { 2 } } \} ^ { \frac { 1 } { 2 } }" align="absmiddle" class="latex-formula">solve this equation
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Answer 1

Answer:

Step-by-step explanation:

Exponent law:

    $\sf \bf a^m * a^n = a^{m+n}\\\\ (a^m)^n = a^{m*n}$

    $\sf a^{-m}=\dfrac{1}{a^m}$

       First convert radical form to exponent form and then apply exponent law.

 $\sf \sqrt{3}=3^{\frac{1}{2}}\\\\\sqrt{5}=5^{\frac{1}{2}}$

$\sf \left(\dfrac{(\sqrt{3}*3^{-2}}{(\sqrt{5})^2}\right)^{\frac{1}{2}}= \left(\dfrac{3^{\frac{1}{2}}*3^{-2}}{(5^{\frac{1}{2}})^2} \right )^{\frac{1}{2}}$

                      $= \left(\dfrac{3^{\frac{1}{2}-2}}{5^{\frac{1}{2}*2}}\right)^{\frac{1}{2}}\\\\=\left(\dfrac{3^{\frac{1-4}{2}}}{5}\right)^{\frac{1}{2}}\\\\=\left(\dfrac{3^{\frac{-3}{2}}}{5}\right)^{\frac{1}{2}}\\\\=\dfrac{3^{\frac{-3}{2}*{\frac{1}{2}}}}{5^{\frac{1}{2}}}\\\\ =\dfrac{3^{{\frac{-3}{4}}}}{5^{\frac{1}{2}}}$