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

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Answer 1 · 2016-01-31T01:00:18

The square root is expressed as an exponent of #1/2#, so #sqrt(x^5)# can be expressed as #x^(5/2)#.

Roots are expressed as fractional exponents:

#root(2)x=x^(1/2)#
#root(3)x=x^(1/3)#

and so on.

This makes sense, because when we multiply we add exponents:

#sqrt(x)# x #sqrt(x)# = #x#

#x^(1/2)# x #x^(1/2)# = #x^((1/2+1/2))# = #x^1# = #x#

When an exponent is raised to another exponent, the exponents are multiplied:

#sqrt(x^5)=(x^5)^(1/2) = x^(5*1/2) = x^(5/2)#