How do you simplify (-3^(2/3))(4^(1/4))(−323)(414)?

1 Answer
Shwetank Mauria
May 31, 2017

(-3^(2/3))(4^(1/4))=-root(12)419904=-2.9417(−323)(414)=−12√419904=−2.9417

Explanation:

In fractional exponents we have 33 and 44 as denominators. So let us reduce them to common denominators i.e. 1212 as 1212 is GCD of 33 and 44. Hence

(-3^(2/3))(4^(1/4))(−323)(414)

= (-3^((2xx4)/(3xx4)))(4^((1xx3)/(4xx3)))(−32×43×4)(41×34×3)

= (-3^(8/12))(4^(3/12))(−3812)(4312)

= (-3^8xx4^3)^(1/12)(−38×43)112

= (-6561xx64)^(1/12)(−6561×64)112

= -root(12)419904−12√419904

Incidentally, it is equal to -2.9417−2.9417

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