# multiplying different bases with fractional exponents

by theresa
(USA)

Working with Fractional Exponents

How do you multiply 3 to the 1/2 power by 9 to the 1/3 power to equal 9 to the 7/12 power?

### Comments for multiplying different bases with fractional exponents

 Jan 11, 2014 fractional exponents by: Staff Answer Part I 3^(1/2) * 9^(1/3) since 3 is the square root of 9, then 3 = 9^(1/2) substitute 9^(1/2) for the 3 in the first factor = 9^(1/2)^(1/2) * 9^(1/3) using the distributive property of exponents, the exponent of the first factor can be simplified ^(1/2)^(1/2) = ^((1/2)*(1/2)) = ^(1/4) replace the exponent of the first factor ^(1/2)^(1/2) with the simplified version ^(1/4) = 9^(1/4) * 9^(1/3) --------------------------------------------

 Jan 11, 2014 fractional exponents by: Staff -------------------------------------------- Part II since both factors now have the same base (a base of 9), the exponents are additive 9^((1/4) +(1/3)) 9^((3/12) +(4/12)) 9^(7/12) the final answer is: 3^(1/2) * 9^(1/3) = 9^(7/12) --------------------------------------------

 Jan 11, 2014 fractional exponents by: Staff -------------------------------------------- Part III ------------------------------------------------------------------------- normal simplification process 3^(1/2) * 9^(1/3) 3^(1/2) * (3 * 3)^(1/3) 3^(1/2) * 3^(1/3) * 3^(1/3) 3^(1/2 + 1/3 + 1/3) 3^(3/6 + 2/6 + 2/6) 3^(7/6) 3^(6/6 + 1/6) 3^(6/6) * 3^(1/6) 3^(1) * 3^(1/6) 3 * 3^(1/6) simplified expression: 3^(1/2) * 9^(1/3) = 3 * 3^(1/6) Thanks for writing. Staff www.solving-math-problems.com

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