[tex]\sqrt{{({a}^{\frac{ - 1}{3}} \times {b}^{ \frac{ - 1}{2}} \times c)}^{3}} [/tex]
[tex]= \sqrt{{({(8)}^{\frac{ - 1}{3}} \times {(25)}^{ \frac{ - 1}{2}} \times (10))}^{3}} [/tex]
[tex]= \sqrt{{({({2}^{3})}^{\frac{ - 1}{3}} \times {({5}^{2})}^{ \frac{ - 1}{2}} \times (10))}^{3}}[/tex]
[tex]= \sqrt{{(2)}^{(3)(\frac{ - 1}{3})(3)} \times {(5)}^{(2)(\frac{ - 1}{2})(3)} \times {(10)}^{3}} [/tex]
[tex]= \sqrt{{(2)}^{ - 3} \times {(5)}^{ - 3} \times {(10)}^{3} } [/tex]
[tex]= \sqrt{{(2 \times 5)}^{ - 3} \times {(10)}^{3}} [/tex]
[tex]= \sqrt{{(10)}^{ - 3} \times {(10)}^{3}} [/tex]
[tex]= \sqrt{{(10)}^{( - 3) + 3}} = \sqrt{{(10)}^{0}} = \sqrt{1} = 1[/tex]
[tex]\sqrt { ( ( 8 ) ^ { \frac { - 1 } { 3 } } \times ( 25 ) ^ { \frac { - 1 } { 2 } } \times ( 10 ) ) ^ { 3 } } \\ \\ = \sqrt{\left(8^{-\frac{1}{3}}\times 25^{\frac{-1}{2}}\times 10\right)^{3}} \\ \\ = \sqrt{\left(\frac{1}{2}\times 25^{\frac{-1}{2}}\times 10\right)^{3}} \\ \\ = \sqrt{\left(\frac{1}{2}\times 25^{-\frac{1}{2}}\times 10\right)^{3}} \\ \\ = \sqrt{\left(\frac{1}{2}\times \left(\frac{1}{5}\right)\times 10\right)^{3}} \\ \\ = \sqrt{\left(\frac{1}{10}\times 10\right)^{3}} \\ \\ = \sqrt{1^{3}} \\ \\ = \sqrt{1} \\ \\ = 1[/tex]
[answer.2.content]
