Question

PLEASEE HELP ANYONE WHO IS GOOD AT MATH

Answer 1

$\sqrt{\frac{126xy^{5}}{32x^{3}}}=\sqrt{\frac{63y^{5}}{ax^{b}}}\\\\\sqrt{\frac{63y^{5}}{16x^{2}}}=\sqrt{\frac{63y^{5}}{ax^{b}}}\\\\\frac{\sqrt{63y^{5}}}{\sqrt{16x^{2}}}=\frac{\sqrt{63y^{5}}}{\sqrt{ax^{b}}}\\\\\frac{\sqrt{63y^{5}}}{\sqrt{16x^{2}}}*\frac{1}{\sqrt{63y^{5}}}=\frac{\sqrt{63y^{5}}}{\sqrt{ax^{b}}}*\frac{1}{\sqrt{63y^{5}}}\\\\\frac{1}{\sqrt{16x^{2}}}=\frac{1}{\sqrt{ax^{b}}}\\\\\sqrt{16x^{2}}=\sqrt{ax^{b}}$

Thus for the two equations to be equal, a = 16 and b = 2.

Answer 2

What was done from the first to the second equation was that the fraction was simplified. 126 and 32 have a common factors of 2. 
126/32=(63*2)/(16*2)
The 2s in the top and bottom can cancel out, leaving the fraction 63/16. 
In addition, since there are x terms on the top and bottom, they cancelled out as well. 
x/x^3=1/x^2
This leaves an x^2 term on the bottom. 
Thus, if a is 16, and b is 2, you will have an equivalent form of the fraction.