Question

What is the product of a,b, and c?

Answer 1

`abc = - (16)/(3)`

Explanation:

`{x}^( - 2) {y}^(3) \sqrt[3]{ 64{x}^(5) {y}^(3) } = a {x}^(b) {y}^(c) \\ \\ {x}^( - 2) {y}^(3) * 4 * {x}^{ (5)/(3) } * y= a {x}^(b) {y}^(c) \\ \\ 4 {x}^{ (5)/(3) - 2 } {y}^(3 + 1) = a {x}^(b) {y}^(c) \\ \\ 4 {x}^{ (5 - 6)/(3) } {y}^(4) = a {x}^(b) {y}^(c) \\ \\ 4 {x}^{ ( - 1)/(3) } {y}^(4) = a {x}^(b) {y}^(c) \\ \\ equating \: like \: terms \: on \: both \: sides \\ \\ a = 4 \\ \\ b = - (1)/(3) \\ \\ c = 4 \\ \\ abc = 4 * ( - (1)/(3) ) * 4 \\ \\ = 16 * ( - (1)/(3) ) \\ \\ abc = - (16)/(3)`