Final answer:
The missing exponent in 3?×3−6=32. is 4.
Therefore, correct answer is C. 4
Step-by-step explanation:
To complete the equation 3^x × 3^(-6) = 3², we can apply the rule of exponents, which states that when you multiply two terms with the same base, you add their exponents. In this case, the missing exponent should make the bases match on both sides. Thus, 3^x × 3^(-6) becomes 3^(x - 6). For the equation to equal 3², the exponent (x - 6) must be equal to 2. Solving for x, we find that x = 8. Therefore, the missing exponent is 8, and the completed equation is 3⁸ × 3^(-6) = 3².
Understanding the rules of exponents is crucial in solving equations involving powers. It enables the manipulation of expressions with the same base, facilitating simplification and solution of mathematical problems. Proficiency in exponent rules is fundamental in algebra and various mathematical applications.
Therefore, correct answer is C. 4