Question

PLEASEE HELP ANYONE WHO IS GOOD AT MATH

Find the values of a and b that make the second expression equivalent to the first expression. Assume that x > 0 and y ≥ 0.
A = AND B=

Answer 1

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.

Answer 2

`\sqrt{(126xy^(5))/(32x^(3))}=\sqrt{(63y^(5))/(ax^(b))}\\\\\sqrt{(63y^(5))/(16x^(2))}=\sqrt{(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.