Final answer:
To solve the exponential equation (5/3)ʸ = 125/27, express both 125 and 27 as powers of 5 and 3 respectively, to find that x = 3 provides equality.
Step-by-step explanation:
To solve the equation (5/3)ʸ = 125/27,
Firstly, recognize that both 125 and 27 can be expressed as powers of 5 and 3, respectively. 125 is equal to 5³ and 27 is equal to 3³. Rewrite the equation as:
(5³)/(3³) = (5/3)ʸ
Using the property xPx⁹ = x(p+q), we can infer that if (5/3)ʸ is equal to 5³/3³, then x must be 3 because (5/3)¸ gives us 5 raised to the power of x divided by 3 raised to the power of x; this matches the expression on the left which is 5 cubed divided by 3 cubed.
Therefore, x = 3 is the solution to the given equation.