Question

Find the value of 'a' and 'b' if:

9^2a = `(root(3)(81))^(-6/"b") = (sqrt(27))^2`

Answer 1

9^2a = `(root(3)(81))^(-6/"b") = (sqrt(27))^2`

⇒ 9^2a = `(root(3)(3^4))^(-6/"b") = (sqrt(3^3))^2`

⇒ (3²)^2a = `(3^(4xx1/3))^(-6/"b") = (3^(3xx1/2))^2`

⇒ 3^4a = `(3^1)^(-8/"b") = (3^1)^3`

⇒ 3^4a = `(-8)/"b" = 3`

⇒ 3^4a = 3 and `(-8)/"b"` = 3

⇒ 4a = 3 and b = `(-8)/(3)`

⇒ `"a" = (3)/(4) and "b" = (-8)/(3)`.