How do you write #sqrt(7mn) ^5# as an exponential form?

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Answer 1 · 2017-06-14T12:40:32

#(7mn)^(5/2)#

Use the law of indices which states:

#(root(q)x)^p = x^(p/q)#

The root becomes the denominator of the fraction in the index, and the power becomes the numerator in the fraction:

#root(3)(x^4) = x^(4/3)#

In this case we have:

#(sqrt(7mn))^5 = (7mn)^(5/2)#

Answer 2 · 2017-06-14T12:43:51

#sqrt(7mn)^5=color(red)((7mn)^(5/2)#

#sqrt(7mn)^5= (sqrt(7mn))^5# (at least that's what I assumed was meant by the question)

#color(white)("XXX")=((7mn)^(1/2))^5#

#color(white)("XXX")=(7mn)^(5/2)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

If this were intended to be the 5th root, it should have been written as:
#color(white)("XXX")root(5)(7mn)#

If the 5 were to apply only to the #n# then it should appear under the radical sign as
#color(white)("XXX")sqrt(7mn^5)#