Question

SqrR(3x^12 * y^10) / SqrR(5x^6 * y^3)

A. 5x3y3square root fifteen y
B. x cubed y cubed square root fifteen y over five
C. square root of fifteen x to the eighteenth y to the thirteenth over five x to the six times y cubed

D. none of these

Answer 1

What we are going to do in this case is to simplify the expression step by step.
We have then:
SqrR (3x ^ 12 * y ^ 10) / SqrR (5x ^ 6 * y ^ 3)
SqrR (3x ^ 12 * y ^ 10 * y) / SqrR (5x ^ 6 * y ^ 3 * y)
We use square root properties:
((x ^ 6 * y ^ 5) * SqrR (3y)) / ((x ^ 3 * y ^ 2) * SqrR (5))
We use power properties:
((x ^ (6-3) * y ^ (5-2)) * SqrR (3y)) / (SqrR (5))
((x ^ 3 * y ^ 3) * SqrR (3y)) / (SqrR (5))
((x ^ 3 * y ^ 3) * SqrR (15y)) / (SqrR (25))
1/5 * ((x ^ 3 * y ^ 3) * SqrR (15y))
Answer:
D. none of these