document.write( "Question 423081: I need help with this problem. Thank you.
\n" ); document.write( "Write the given function in the form y=ab^x\r
\n" ); document.write( "\n" ); document.write( " $\"y=+sqrt%289%5E%28x-1%29%29\"$ \n" ); document.write( "

Algebra.Com's Answer #295209 by jsmallt9(3759) $\"\"$ $\"About$

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$\"y=+sqrt%289%5E%28x-1%29%29\"$
\n" ); document.write( "Since the desired form has no square roots, we will start by eliminating the square root. We can replace the square root with an exponent of 1/2. Because of occasional display problems with fractional exponents I am going to use the decimal equivalent of 1/2, 0.5:
\n" ); document.write( " $\"y=+%289%5E%28x-1%29%29%5E0.5\"$
\n" ); document.write( "We now have a power of a power of 8. The rule for exponents for this is to multiply the exponents:
\n" ); document.write( " $\"y=++9%5E%28%28x-1%29%2A0.5%29\"$
\n" ); document.write( "We still want an exponent of just x. So we need still to eliminate the -1 and the 0.5. Since $\"9+=+3%5E2\"$ we can introduce a 2 into the exponent:
\n" ); document.write( " $\"y=++%283%5E2%29%5E%28%28x-1%29%2A0.5%29\"$
\n" ); document.write( "Again we use the rule for exponents:
\n" ); document.write( " $\"y=++3%5E%282%2A%28x-1%29%2A0.5%29\"$
\n" ); document.write( "The exponent simplifies to:
\n" ); document.write( " $\"y=++3%5E%28x-1%29\"$
\n" ); document.write( "We're making progress. All we have to do now is eliminate the -1. The exponent is now a subtraction. And when do we subtract exponents? Answer: When we divide. So if we \"undo\" a division involving $\"3%5Ex\"$ and $\"3%5E1\"$ ...
\n" ); document.write( " $\"y=++3%5Ex%2F3%5E1\"$
\n" ); document.write( "The denominator simplifies:
\n" ); document.write( " $\"y=++3%5Ex%2F3\"$
\n" ); document.write( "The exponent is finally what we want it to be. But we want something times $\"3%5Ex\"$ not $\"3%5Ex\"$ divided by something. Since division by 3 is the same as multiplying by the reciprocal of 3 this is an easy checge:
\n" ); document.write( " $\"y=++%281%2F3%293%5Ex\"$
\n" ); document.write( "We finally have the desired form with the \"a\" being 1/3 and the \"b\" being 3.

\n" ); document.write( "P.S. In response to the question in your \"Thank you\"...
\n" ); document.write( "The problem asked for an equation of the form:
\n" ); document.write( " $\"y+=+a%2Ab%5Ex\"$
\n" ); document.write( "With the steps I've shown above we've transformed
\n" ); document.write( " $\"y=+sqrt%289%5E%28x-1%29%29\"$
\n" ); document.write( "into
\n" ); document.write( " $\"y+=+%281%2F3%29%2A3%5Ex\"$
\n" ); document.write( "which is the desired form. So I don't understand your question: \"Does x stay the exponent?\" First of all, the desired form wants the exponent to be x so we don't want the exponent to stop being x. Second, I'm not sure where the \"x\" can go. (Remember, the order of operations (aka PEMDAS) requires that we raise 3 to the x power before we multiply by 1/3. So the 1/3 and the 3 do not cancel.) \n" ); document.write( "

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