# SOLUTION: I need help with this problem. Thank you. Write the given function in the form y=ab^x {{{y= sqrt(9^(x-1))}}}

Algebra ->  -> SOLUTION: I need help with this problem. Thank you. Write the given function in the form y=ab^x {{{y= sqrt(9^(x-1))}}}      Log On

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 Question 423081: I need help with this problem. Thank you. Write the given function in the form y=ab^x Answer by jsmallt9(3438)   (Show Source): You can put this solution on YOUR website! 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: We now have a power of a power of 8. The rule for exponents for this is to multiply the exponents: We still want an exponent of just x. So we need still to eliminate the -1 and the 0.5. Since we can introduce a 2 into the exponent: Again we use the rule for exponents: The exponent simplifies to: 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 and ... The denominator simplifies: The exponent is finally what we want it to be. But we want something times not divided by something. Since division by 3 is the same as multiplying by the reciprocal of 3 this is an easy checge: We finally have the desired form with the "a" being 1/3 and the "b" being 3. P.S. In response to the question in your "Thank you"... The problem asked for an equation of the form: With the steps I've shown above we've transformed into 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.)