[tex] {2}^{ {x}^{ - 7} } = \frac{1}{32} [/tex]
[tex] {2}^{ \frac{1}{ {x}^{7} } } = {32}^{ - 1} [/tex]
[tex] {2}^{ \frac{1}{ {x}^{7} } } = ( {2}^{5} {)}^{ - 1} [/tex]
[tex] {2}^{ \frac{1}{ {x}^{7} } } = {2}^{ - 5} [/tex]
[tex] \frac{1}{ {x}^{7} } = - 5[/tex]
[tex] {x}^{7} = - \frac{1}{5} [/tex]
[tex]x =\small\boxed{ \sqrt[7]{ - \frac{1}{5} } }[/tex]
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[tex] {2}^{ {x}^{ - 7} } = \frac{1}{32} [/tex]
[tex] {2}^{ \frac{1}{ {x}^{7} } } = {32}^{ - 1} [/tex]
[tex] {2}^{ \frac{1}{ {x}^{7} } } = ( {2}^{5} {)}^{ - 1} [/tex]
[tex] {2}^{ \frac{1}{ {x}^{7} } } = {2}^{ - 5} [/tex]
[tex] \frac{1}{ {x}^{7} } = - 5[/tex]
[tex] {x}^{7} = - \frac{1}{5} [/tex]
[tex]x =\small\boxed{ \sqrt[7]{ - \frac{1}{5} } }[/tex]