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
$color(white)("XXX")sqrt(7mn^5)$

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