Final answer:
The given equation 6^5 = 6 x × 6^4 is solved by recognizing that the exponents of the same base are additive. Thus, x equals 1, making option a) the correct answer.
Step-by-step explanation:
Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself. For example, 6 is multiplied by itself 4 times, i.e. 6 × 6 × 6 × 6. The student has asked the following question: 65 = 6 x × 64. Solve for x. The options are a) 1, b) 2, c) 3, d) 4. To solve for x, let's simplify the equation by using the power of a product rule, which states that (am)n = am×n. According to this rule, if we have 61, which is just 6, multiplied by 64, the exponents add together (because the bases are the same). So, 61+4 = 65, indicating that x must be 1 since that's the exponent of the first 6.
Therefore, the answer is a) 1, as it satisfies the equation 65 = 6 × 64.