Question 517698: Does 3^5+3^5+3^5= 3^6. Please explain.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The answer to this question is "Yes".
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3^5 equals 3*3*3*3*3 = 243
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So:
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3^5+3^5+3^5 = 243 + 243 +243 = 729
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But also:
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3^6 = 3*3*3*3*3*3 = 729
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The reason for this may be easier to see if you start with the original expression:
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3^5 + 3^5 + 3^5
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Substitute X for 3^5 and this expression becomes:
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X + X + X
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But this expression adds up to be 3X.
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Now replace the X with its equal 3^5 and you can see that you now have
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3*3^5
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The multiplier 3 has an implied exponent of 1. So this expression is equivalent to:
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3^1 * 3^5
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And, since both multipliers have the base 3, you multiply them by adding the exponents:
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3^1 * 3^5 = 3^(1+5) = 3^6
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Hope this helps you to see why:
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3^5+3^5+3^5 = 3*3^5 = 3^6
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