Final answer:
The student's question involves solving an equation that could be related to exponents or linear equations. Using the provided examples, it illustrates how to apply the exponent rule that combines powers of the same base and how to manipulate equations to isolate and solve for a variable.
Step-by-step explanation:
The student's question pertains to solving for a variable in an equation. To solve the equation 129 = 7x 73, we need to clarify the equation structure. However, based on the provided information about discovering rules through experimentation, we can deduce that the equation might involve exponents. The rule illustrated in the examples suggests that for an expression like x^p · x^q, the result is x^(p+q). For example, if asked to solve (7^4)^3, we would calculate this by cubing 7 to the 4th power, effectively multiplying the exponents to get 7^(4×3), which is 7^12. Similarly, with 3^2 · 3^5, we would add the exponents to get 3^7. To solve linear equations like 7y = 6x + 8 and y + 7 = 3x, we would rearrange the equation to isolate y and solve for it in terms of x. This understanding of rules can be applied to solve various mathematical problems, confirming the flexibility and consistency of mathematical principles.