logo for solving-math-problems.com
leftimage for solving-math-problems.com

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

Click here to add your own comments

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)



substitute 9^(1/2), the square root of  9,  for the number 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)



simplify the first factor using the distributive law of exponents





--------------------------------------------

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)



add the exponents





the final answer is:

3^(1/2) * 9^(1/3) = 9^(7/12)



final answer - multiplying different bases with fractional exponents









--------------------------------------------

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


Sep 28, 2016
this is your final chance NEW
by:

give me my money or else. You people are pathetic. GIVE ME THAT MONEY

Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Math Questions & Comments - 01.



Copyright © 2008-2015. All rights reserved. Solving-Math-Problems.com