How do you write with fractional exponents for #(4)(sqrt(y^3))#?

2 Answers
Apr 10, 2015

Things to remember
#sqrt(y^3) = (sqrt(y))^3#
#sqrt(a) = a^(1/2)#
and
#(p^q)^r = p^(qr)#

Therefore
#(4)sqrt(y^3))#

#= (4) (sqrt(y))^3#

#= (4) (y^(1/2))^3#

#= 4 y ^(3/2)#

Apr 10, 2015

4y^#(3/2)#

Square root means exponent is #1/2# of every number inside the radical sign. Hence the exponent 3 would become #3/2# when radical sign is dispensed with.