Question 697208
a general rule is:
{{{ a^(-b) = (1/a)^b }}}
So, you have
{{{ a = 16/81 }}}
{{{ -b = -1/4 }}}
and
{{{ 1/a = 81/16 }}}
{{{ b = 1/4 }}}
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{{{ ( 16/81 )^(-1/4) = ( 81/16 )^(1/4) }}}
and, since
{{{ 81/16 = ( 3*3*3*3 ) / ( 2*2*2*2 ) }}}, then
{{{( 81/16 )^(1/4) = 3/2 }}}
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You can check it on your calculator:
{{{ 16/81 = .19753 }}}
Now do {{{ .19753^(-.25) = 1.5 }}}