Question 1035220
{{{ (1/3)^(-3) = 27^(-x) }}}
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You can use the rule:
{{{ ( a^b )*( a^(-b) ) = a^(( b - b )) }}}
{{{ a^(( b-b )) = a^0 }}}
{{{ a^0 = 1 }}}
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Multiply both sides by {{{ (1/3)^3 }}}
{{{ (1/3)^(-3)*(1/3)^3 = 27^(-x)*(1/3)^3 }}}
{{{ 1 = 27^(-x)*(1/3)^3 }}}
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Multiply both sides by {{{ 27^x }}}
{{{ 27^x = 27^(-x)*27^x *(1/3)^3 }}}
{{{ 27^x = 1*(1/3)^3 }}}
{{{ 27^x = 1/27 }}}
Multiply both sides by {{{ 27^1 }}}
{{{ 27^1*27^x = 1 }}}
{{{ 27^( x + 1 ) = 1 }}}
{{{ 27^( -1 + 1 ) = 1 }}}
{{{ 27^0 = 1 }}}
{{{ 1 = 1 }}}
So, {{{ x = -1 }}}
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check the answer
{{{ (1/3)^(-3) = 27^(-x) }}}
{{{ (1/3)^(-3) = 27^(-(-1)) }}}
{{{ (1/3)^(-3) = 27^1 }}}
{{{ (1/3)^(-3)*(1/3)^3 = 27*(1/3)^3 }}}
{{{ 1 = 27*( 1/27 ) }}}
{{{ 1 = 1 }}}
OK