Question 1014758
Hi,
I think you want to know the basics of how
to raise a power to a power.
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I'll show you a more simple example.
{{{ ( 3^5)^3 }}}
This is the same as:
{{{ ( 3*3*3*3*3 )*( 3*3*3*3*3 )*( 3*3*3*3*3 ) }}}
So, just get rid of the parentheses and you have:
{{{ (3^5)^3 = 3^15 }}}
also:
{{{ ( 3^3 )^5 = 3^15 }}}
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So, in general,
{{{ ( x^a )^b = x^( a*b ) }}}
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Your problem is:
{{{ ( 4^(-3) )^4 }}}
{{{ x = 4 }}}
{{{ a = -3 }}}
{{{ b = 4 }}}
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{{{ ( 4^(-3) )^4 = 4^(-12 ) }}} answer
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Also, according to what I stated:
{{{ ( 4^(-3))^4 = (4^4)^(-3) }}}
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Writing this out the long way:
{{{ (( 1/4 )*( 1/4 )*( 1/4 ))^4 = ( 4*4*4*4 )^(-3) }}}
{{{ ( 1/64 )^4 = 256^(-3) }}}
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For the right side:
{{{ x^(-a) = 1/( x^a ) }}}
{{{ 256^(-3) - 1/256^3 }}} so,
{{{ 1/64^4 = 1/256^3 }}}
{{{ 1/16777216 = 1/16777216 }}}
and those should also be the same as my answer:
{{{ 4^(-12) = 1/16777216 }}}
Hope I didn't throw too much at you
exponents can be challenging