document.write( "Question 517698: Does 3^5+3^5+3^5= 3^6. Please explain. \n" ); document.write( "
Algebra.Com's Answer #344877 by bucky(2189)\"\" \"About 
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The answer to this question is \"Yes\".
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\n" ); document.write( "3^5 equals 3*3*3*3*3 = 243
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\n" ); document.write( "So:
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\n" ); document.write( "3^5+3^5+3^5 = 243 + 243 +243 = 729
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\n" ); document.write( "But also:
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\n" ); document.write( "3^6 = 3*3*3*3*3*3 = 729
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\n" ); document.write( "The reason for this may be easier to see if you start with the original expression:
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\n" ); document.write( "3^5 + 3^5 + 3^5
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\n" ); document.write( "Substitute X for 3^5 and this expression becomes:
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\n" ); document.write( "X + X + X
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\n" ); document.write( "But this expression adds up to be 3X.
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\n" ); document.write( "Now replace the X with its equal 3^5 and you can see that you now have
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\n" ); document.write( "The multiplier 3 has an implied exponent of 1. So this expression is equivalent to:
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\n" ); document.write( "3^1 * 3^5
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\n" ); document.write( "And, since both multipliers have the base 3, you multiply them by adding the exponents:
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\n" ); document.write( "3^1 * 3^5 = 3^(1+5) = 3^6
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\n" ); document.write( "Hope this helps you to see why:
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\n" ); document.write( "3^5+3^5+3^5 = 3*3^5 = 3^6
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