document.write( "Question 230622: How do I solve for a varaible with a decimal exponent?\r
\n" ); document.write( "\n" ); document.write( "x^0.725 = 41.494 \n" ); document.write( "
Algebra.Com's Answer #170802 by jsmallt9(3759)\"\" \"About 
You can put this solution on YOUR website!
\"x%5E0.725+=+41.494\"
\n" ); document.write( "Since the goal is to have an equation that says:
\n" ); document.write( "x = some number
\n" ); document.write( "Since the exponent on x is 1, we can look at the problem as: \"How do I change an exponent of 0.725 to a 1?\" One way we could do this is to raise both sides to the 1/0.725 power. Let's see:
\n" ); document.write( "\"%28x%5E0.725%29%5E%281%2F0.725%29+=+%2841.494%29%5E%281%2F0.725%29\"
\n" ); document.write( "The left side works out to be x because
  • \"%28a%5Eb%29%5Ec+=+a%5E%28bc%29\"
  • 0.725 and 1/0.725 are reciprocals
  • When you multiply reciprocals you always get 1
  • \"x%5E1+=+x\"

\n" ); document.write( "So we have
\n" ); document.write( "\"x+=+%2841.494%29%5E%281%2F0.725%29\"
\n" ); document.write( "We can use our calculators to find the right side. (It works out to be approximately 170.4919451462086020.) \n" ); document.write( "
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