How do you simplify #sqrt(w^14)#?

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Answer 1 · 2015-09-30T10:44:06

# = color(blue)(w^7#

#sqrt(w^14)#

Square root , can also be called as second root or a half power (#color(blue)(1/2#)

so , #sqrt (w^14) = (w^14)^(color(blue)(1/2)#

# = color(blue)(w^7#

Answer 2 · 2015-10-01T22:31:07

#sqrt(w^14) = abs(w^7)#

If #a >= 0# then #sqrt(a^2) = a#

If #a >= 0# and #b, c > 0# then #(a^b)^c = a^(bc)#

So if #w >= 0# then:

#sqrt(w^14) = sqrt((w^7)^2) = w^7#

and if #w < 0# then:

#sqrt(w^14) = sqrt((-w)^14) = sqrt(((-w)^7)^2) = (-w)^7 = -w^7#

So in both cases we have

#sqrt(w^14) = abs(w^7)#