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Question
Find the value of 'a' and 'b' if:
92a = `(root(3)(81))^(-6/"b") = (sqrt(27))^2`
Solution
92a = `(root(3)(81))^(-6/"b") = (sqrt(27))^2`
⇒ 92a = `(root(3)(3^4))^(-6/"b") = (sqrt(3^3))^2`
⇒ (32)2a = `(3^(4xx1/3))^(-6/"b") = (3^(3xx1/2))^2`
⇒ 34a = `(3^1)^(-8/"b") = (3^1)^3`
⇒ 34a = `(-8)/"b" = 3`
⇒ 34a = 3 and `(-8)/"b"` = 3
⇒ 4a = 3 and b = `(-8)/(3)`
⇒ `"a" = (3)/(4) and "b" = (-8)/(3)`.
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