For this case we must find the values of "a" and "b" that make the expressions equivalent:
We have:
![\sqrt {\frac {126xy ^ 5} {32x ^ 3}} =](https://img.qammunity.org/2020/formulas/mathematics/middle-school/t6drhy3gvm07erppqhl53cpl2ocsh6saju.png)
We take common factor "2" from the numerator and denominator:
![\sqrt {\frac {2 * (63xy ^ 5)} {2 * (16x ^ 3)}} =](https://img.qammunity.org/2020/formulas/mathematics/middle-school/qrnugzeimukpntbg4pyd2ib5lxrgdih38q.png)
Eliminating common factors of numerator and denominator:
![\sqrt {\frac {63y ^ 5} {16x ^ 2}} =](https://img.qammunity.org/2020/formulas/mathematics/middle-school/he5lihc5g4s0wsosoxxh0deemn7535thxe.png)
So, we have that the values of a and b are:
![a = 16\\b = 2](https://img.qammunity.org/2020/formulas/mathematics/middle-school/xtmdb1sqxnfree3pm3nxf3g79jdp0oay2u.png)
Answer:
![a = 16\\b = 2](https://img.qammunity.org/2020/formulas/mathematics/middle-school/xtmdb1sqxnfree3pm3nxf3g79jdp0oay2u.png)
Note: To write square root on pc we use sqrt