Final answer:
The expression (x^14)(x^7)^4 simplifies to x^42, so the value of a is 42.
Step-by-step explanation:
To solve for the value of a in the expression (x14)(x7)4, we apply the rules of exponents, particularly the power rule which states that (xa)b = xa·b. First, we simplify (x7)4 by multiplying the exponents, which gives us x28. Next, we can combine x14 and x28 using the product rule for exponents (adding the exponents for the same base during multiplication):
x14 · x28 = x14+28 = x42
Therefore, the expression (x14)(x7)4 is equivalent to x42, which means a = 42.