Final answer:
The solution involves using exponent rules: when multiplying like bases, add the exponents. For the equation 3ʸ times 3⁵ = 3⁷, we find that x + 5 = 7, and thus, x = 2.
Step-by-step explanation:
The question asks to solve the equation 3ʸ times 3⁵ = 3⁷ for the variable x. According to the properties of exponents, when we multiply numbers with the same base, we add their exponents. Therefore, the given equation can be rewritten using this rule as 3(x+5) = 3⁷. To find the value of x, we set the exponents equal to each other because the bases are the same, which gives us x + 5 = 7. Solving for x, we subtract 5 from both sides, yielding x = 7 - 5, thus x = 2.
This conceptual rule is also applicable when dealing with more complex expressions like 3².35, where we would apply similar strategies of exponent manipulation.