Simplify the given expression.
$$(13^2-5^2 )^{(\frac{3}{2})}×8^{\frac{2}{3})}÷\left(\frac{1}{6}\right)^{(-3)}$$​

Correct option is C

Given:

​$$(13^2-5^2 )^{(\frac{3}{2})}×8^{\frac{2}{3})}÷\left(\frac{1}{6}\right)^{(-3)}$$​​

Formula Used:

​$$x^{-a} = \frac{1}{x^a}$$​​

​$$x^{\frac{1}{3}} = \sqrt[3]{x}$$​​

​$$(a^2 - b^2 ) =(a+b)(a-b)$$​​

Solution:

​$$(13^2-5^2 )^{(\frac{3}{2})}×8^{\frac{2}{3})}÷\left(\frac{1}{6}\right)^{(-3)}$$​​

= $$((13-5)(13+5) )^{(\frac{3}{2})}×(\sqrt[3]{8})^2 ÷6^3$$​​

= $$((8)(18) )^{(\frac{3}{2})}×(2)^2 ÷216$$​​

= $$(\sqrt{144} )^3×(2)^2 ÷216$$​​

= $$(12 )^3×(2)^2 ÷216$$​​

= $$\frac{1728 ×4}{216}$$​​

= 32

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