How do you simplify #(-3^(2/3))(4^(1/4))#?

1 Answer
Shwetank Mauria
May 31, 2017

#(-3^(2/3))(4^(1/4))=-root(12)419904=-2.9417#

Explanation:

In fractional exponents we have #3# and #4# as denominators. So let us reduce them to common denominators i.e. #12# as #12# is GCD of #3# and #4#. Hence

#(-3^(2/3))(4^(1/4))#

= #(-3^((2xx4)/(3xx4)))(4^((1xx3)/(4xx3)))#

= #(-3^(8/12))(4^(3/12))#

= #(-3^8xx4^3)^(1/12)#

= #(-6561xx64)^(1/12)#

= #-root(12)419904#

Incidentally, it is equal to #-2.9417#

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