Question

How do solve this?? please

Answer 1

m = - 3

n = 2

Explanation:

It can be solved using laws of exponents as given below:

`5 {x}^(n) y(2 {x}^(4) {y}^(m) ) = \frac{10 {x}^(6) }{ {y}^(2) } \\ \\ (5 {x}^(n) .2 {x}^(4) )(y. {y}^(m) ) = 10 {x}^(6) {y}^( - 2) \\ \\\cancel {10}\:\: {x}^(n + 4) . {y}^(m + 1) = \cancel {10}\:\: {x}^(6) {y}^( - 2) \\ \\ {x}^(n + 4) . {y}^(m + 1) = {x}^(6) {y}^( - 2) \\equating \: like \: terms \: on \: both \: sides \\ \\ {x}^(n + 4) = {x}^(6) \\ \\ \implies \: n + 4 = 6 \\ \\ n = 6 - 4 \\ \\ \huge \red{n = 2} \\ \\ {y}^(m + 1) = {y}^( - 2) \\ \\ \implies \: m + 1 = - 2 \\ \\ m = - 2 - 1 \\ \\ \huge \purple{m = - 3}`