document.write( "Question 1206763: Why does a base number to the exponent of zero equals 1?
\n" ); document.write( "When a number is multiplied zero times, shouldn't it be zero?\r
\n" ); document.write( "\n" ); document.write( "Example: 10 (exponent zero) = 1.
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Algebra.Com's Answer #844399 by math_tutor2020(3816) $\"\"$ $\"About$

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\n" ); document.write( "Use the ^ key to indicate exponents.
\n" ); document.write( "Something like 10^2 means \"10 squared\" aka $\"10%5E2\"$
\n" ); document.write( "On the keyboard, you find this symbol by holding \"shift\" then pressing the \"6\". \r
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\n" ); document.write( "\n" ); document.write( "If 10^0 = 0 was the case, then multiplying both sides by 10 would get us the following:
\n" ); document.write( "10^0 = 0
\n" ); document.write( "10*10^0 = 10*0
\n" ); document.write( "10^1*10^0 = 0
\n" ); document.write( "10^(1+0) = 0 ............ use rule a^b*a^c = a^(b+c)
\n" ); document.write( "10^1 = 0
\n" ); document.write( "10 = 0
\n" ); document.write( "We run into a problem.
\n" ); document.write( "The two sides don't agree on the same number, in which we consider the last equation to be false.
\n" ); document.write( "The last equation being false makes 10^0 = 0 false.\r
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\n" ); document.write( "\n" ); document.write( "But if 10^0 = 1 was the case, then we don't have any issues.
\n" ); document.write( "10^0 = 1
\n" ); document.write( "10*10^0 = 10*1
\n" ); document.write( "10^1*10^0 = 10
\n" ); document.write( "10^(1+0) = 10
\n" ); document.write( "10^1 = 10
\n" ); document.write( "10 = 10
\n" ); document.write( "The two sides match up to form a true equation at the end.
\n" ); document.write( "The true equation at the end leads to a domino effect to make the first equation true.\r
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\n" ); document.write( "\n" ); document.write( "When going from something like 10^2 to 10^3 we multiply by 10.
\n" ); document.write( "Going in reverse from 10^3 to 10^2 we divide by 10.
\n" ); document.write( "10^2 to 10^1 is also \"divide by 10\".
\n" ); document.write( "And so on. \r
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\n" ); document.write( "\n" ); document.write( "Here's a chart of select values.
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10^3	1000
10^2	100
10^1	10
10^0	1
10^(-1)	1/10 = 0.1
10^(-2)	1/(10^2) = 1/100 = 0.01
10^(-3)	1/(10^3) = 1/1000 = 0.001

\n" ); document.write( "Multiply by 10 to move up the chart.
\n" ); document.write( "Divide by 10 to move down the chart.\r
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\n" ); document.write( "\n" ); document.write( "Here is the more general approach using any base b, where b is nonzero.
\n" ); document.write( "b^0 = 1
\n" ); document.write( "b*b^0 = b*1
\n" ); document.write( "b^1*b^0 = b
\n" ); document.write( "b^(1+0) = b
\n" ); document.write( "b^1 = b
\n" ); document.write( "b = b\r
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\n" ); document.write( "\n" ); document.write( "Once again, b is nonzero.
\n" ); document.write( "If b = 0 was the case, then weird things start to happen and that's a very lengthy discussion for another day (and another class).
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