Final answer:
The correct exponential form of (7√x)^3 is c) 343x¹½, resulting from cubing the coefficient 7 and multiplying the exponent ½ of x by 3.
Step-by-step explanation:
The exponential form of (7√x)^3 can be calculated by cubing the digit term in the usual way and multiplying the exponent of the exponential term by 3. When you apply the power to both the coefficient (7) and the variable (x) with its fractional exponent (½), you get:
(7√x)³ = (7³)(x¹/²)³ = (7*7*7)(x^(1/2*3)) = 343x¹¹/² = 343x¹½.
The correct exponential form of (7√x)^3 is 343x¹½, which makes option c) 343x¹½ the correct answer.