\(\displaystyle \frac{ 1 }{( - 8 ) ^ {\frac{ - 1 }{ 3 }}} + \frac{ 1 }{( - 32 ) ^ {\frac{ - 1 }{ 5 }}} - \frac{ 1 }{( - 64 ) ^ {\frac{ - 1 }{ 3 }}}\)
Solution
[imath]\begin{array}{llllllll} \frac{ 1 }{( - 8 ) ^ {\frac{ - 1 }{ 3 }}} + \frac{ 1 }{( - 32 ) ^ {\frac{ - 1 }{ 5 }}} - \frac{ 1 }{( - 64 ) ^ {\frac{ - 1 }{ 3 }}} \\[11pt] \newline = \frac{ 1 }{\frac{ 1 }{( - 8 ) ^ {\frac{ 1 }{ 3 }}}} + \frac{ 1 }{\frac{ 1 }{( - 32 ) ^ {\frac{ 1 }{ 5 }}}} - \frac{ 1 }{\frac{ 1 }{( - 64 ) ^ {\frac{ 1 }{ 3 }}}} \\[14pt] \newline = \frac{ 1 }{\frac{ 1 }{ \left( ( - 2 ) ^ { 3 } \right) ^ {\frac{ 1 }{ 3 }}}} + \frac{ 1 }{\frac{ 1 }{ \left( ( - 2 ) ^ { 5 } \right) ^ {\frac{ 1 }{ 5 }}}} - \frac{ 1 }{\frac{ 1 }{ \left( ( - 2 ) ^ { 6 } \right) ^ {\frac{ 1 }{ 3 }}}} \\[14pt] \newline =\frac{\frac{ 1 }{ 1 }}{ - 2 } + \frac{\frac{ 1 }{ 1 }}{ - 2 } - \frac{\frac{ 1 }{ 1 }}{( - 2 ) ^ { 2 }} \\[8pt] = - 2 + (- 2 ) - ( - 2 ) ^ { 2 } \\ = - 2 - 2 - (+4) \\ = -4 - 4 = - 8 \end{array}[/imath]
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Solution
[imath]\begin{array}{llllllll} \frac{ 1 }{( - 8 ) ^ {\frac{ - 1 }{ 3 }}} + \frac{ 1 }{( - 32 ) ^ {\frac{ - 1 }{ 5 }}} - \frac{ 1 }{( - 64 ) ^ {\frac{ - 1 }{ 3 }}} \\[11pt] \newline = \frac{ 1 }{\frac{ 1 }{( - 8 ) ^ {\frac{ 1 }{ 3 }}}} + \frac{ 1 }{\frac{ 1 }{( - 32 ) ^ {\frac{ 1 }{ 5 }}}} - \frac{ 1 }{\frac{ 1 }{( - 64 ) ^ {\frac{ 1 }{ 3 }}}} \\[14pt] \newline = \frac{ 1 }{\frac{ 1 }{ \left( ( - 2 ) ^ { 3 } \right) ^ {\frac{ 1 }{ 3 }}}} + \frac{ 1 }{\frac{ 1 }{ \left( ( - 2 ) ^ { 5 } \right) ^ {\frac{ 1 }{ 5 }}}} - \frac{ 1 }{\frac{ 1 }{ \left( ( - 2 ) ^ { 6 } \right) ^ {\frac{ 1 }{ 3 }}}} \\[14pt] \newline =\frac{\frac{ 1 }{ 1 }}{ - 2 } + \frac{\frac{ 1 }{ 1 }}{ - 2 } - \frac{\frac{ 1 }{ 1 }}{( - 2 ) ^ { 2 }} \\[8pt] = - 2 + (- 2 ) - ( - 2 ) ^ { 2 } \\ = - 2 - 2 - (+4) \\ = -4 - 4 = - 8 \end{array}[/imath]
Is my solution correct?
Am not sure if work is correct. Please help me check.