document.write( "Question 1105179: If m and p are positive integers and (2√2)^m = 32^p, what is the value of p/m ? \n" ); document.write( "

Algebra.Com's Answer #719985 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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If m and p are positive integers and (2√2)^m = 32^p,
\n" ); document.write( " what is the value of p/m?
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\n" ); document.write( " $\"%282sqrt%282%29%29%5Em+=+32%5Ep\"$
\n" ); document.write( "we can write both sides as power of 2
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\n" ); document.write( " $\"2%5E%28%283m%29%2F2%29\"$ = $\"2%5E%285p%29\"$ ; that's 3m/2
\n" ); document.write( "therefore
\n" ); document.write( " $\"%283m%29%2F2\"$ = $\"5p\"$
\n" ); document.write( "multiply both sides by 2
\n" ); document.write( "3m = 10p
\n" ); document.write( "\"What is the value of p/m\"
\n" ); document.write( " $\"p%2Fm\"$ = $\"3%2F10\"$
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\n" ); document.write( "Check this with original equation, replacing m and p, use a calc
\n" ); document.write( " $\"%282sqrt%282%29%29%5E10\"$ = $\"32%5E3\"$
\n" ); document.write( "32768 = 32768 \n" ); document.write( "

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