Question 1131439: Simplify
a) √(32k^(7)q^(8))
b)³√(-64a^(8))
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! break it apart
sqrt(32)=sqrt(2)(sqrt(16))=4 sqrt(2)
every 2 in an exponent under the radical (if square root) may be removed and become the variable to the first power. sqrt(k^7) becomes k^3*sqrt(k), the remainder left behind.
sqrt(q^8)=q^4.
multiply everything together to get 4*k^3*q^4*sqrt(2k), noting how the two radical terms are just combined under one radical
do the same for cube roots
cube root of -64 is -4
for cube root of a^8, pull THREE a's out and make it the variable to the first power.
cube root of a^8=a^2*cube root (a^2), the remainder is 2.
This is -4a^2 cube root (a^2)
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