Final answer:
To solve X⁵/7×X¹/², we add the exponents after finding a common denominator, which results in X¹¹/², matching option a).
Step-by-step explanation:
When we have an expression like X⁵/7×X¹/², we can use the property of exponents that states when multiplying with the same base, you add the exponents. The expression can then be rewritten as X^(5/7+1/2). To add these fractions, they need to have a common denominator. The common denominator for 7 and 2 is 14. Thus, we convert 5/7 to 10/14 and 1/2 to 7/14. Now, we can add the exponents: 10/14 + 7/14 = 17/14, which simplifies to X¹¹/² or X¹¹/² in rational exponent form. This matches option a).