Question 829745
{{{ ( 27^(-2/3) ) / ( 27^( -1/3) ) }}}
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First use the general rules:
{{{ a^(-b) = 1/a^b }}}
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Now what if you changed the right side to this:
{{{ 1/a^(-b) }}}
What change would you have to make to the left side?
{{{ a^(-(-b) ) }}} is the change which is
{{{ a^b }}}, so now I have:
{{{ a^b = 1/a^(-b) }}}
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I can rewrite the problem as:
{{{ ( 27^(-2/3) )*( 1/( 27^(-1/3))) }}}
Now I can use the above general rule and rewrite as:
{{{ ( 27^(-2/3) )*( 27^(1/3) ) }}}
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Now use the general rule:
{{{ a^b * a^c = a^( b+ c ) }}}
{{{ 27^( -2/3 + 1/3 ) }}}
{{{ 27^(-1/3) }}}
and now, using:
{{{ a^(-b) = 1/a^b }}}
{{{ 27^(-1/3) = 1 / 27^( 1/3) }}}
{{{ 1/27^(1/3) = 3 }}} answer
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My advice is to list the general rules that you
know in the form that I did and compare them
to the factors in your problem. Keep heading
in the direction of getting rid of minus
signs where you can.
Good luck