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The problem as given: $(4m^3n)^\frac{1}{4} \times (8mn^3)^\frac{1}{2}$

distributed the exponted threw.

$(4^{1/4}m^{3/4}n^{1/4})(8^{1/2}m^{1/2}n^{3/2})$

Then because $a^na^m = a^{n+m} \; \& \; a^{n}b^{n} = (ab)^n$

$(2^2)^{1/4} (8^{1/2})(m^{3/4 + 1/2})( n^{1/4+6/4}) = 16^{1/2}(m^{5/4})n^{7/4}$

am I correct?

edited to fix mistake pointed out by "Old John"

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    $16^{1/2} = \sqrt{16}$2013-09-21

1 Answers 1

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As pointed out in the comments, your answer looks good. The one thing I would change is that I would replace $16^{1/2}$ with $\sqrt{16}=4$, giving you: $4m^{5/4}n^{7/4}$

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    I tend to just keep the fractional exponent, just because it is easy for me.2013-11-11