Question 852674
{{{ ( 2^6 * 2^4 ) / 2^5 }}}
As long as the base is the same ( 2 in this case ),
Multiplying ADDS the exponents
Dividing SUBTRACTS the exponents
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To see this, just write everything out the long way:
{{{ (( 2*2*2*2*2*2 )*( 2*2*2*2 )) / ( 2*2*2*2*2 ) }}}
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Now rewrite it this way:
{{{ (( 2*2*2*2*2 )*( 2*2*2*2*2 )) / ( 2*2*2*2*2 ) }}}
It's the exact same thing, but now you can see the
cancellation top and bottom. You are left with:
{{{ 2*2*2*2*2 }}}
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Expressed with exponents, what I just did was:
{{{ ( 2^6 * 2^4 ) / 2^5 }}}
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{{{ ( 2^5 * 2^5 ) / 2^5 }}}
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{{{ 2^5 }}}
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And what I just did to get the final exponent = {{{ 5 }}} is
{{{ 6 + 4 - 5 = 5 }}}
or, the same thing in the 2nd step:
{{{ 5 + 5 - 5 = 5 }}}
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Just write everything down the long way if you get
confused, and do the top and bottom cancellation.
Hope this helps