Final answer:
To find the value of (25x^2y^{14})^3, cube the numerical coefficient 25 to get 15625, and multiply the exponents of x and y by 3 to obtain x^6 and y^{42}, resulting in 15625x^6y^{42}.
Step-by-step explanation:
The value of the exponential expression (25x^2y^{14})^3 can be calculated by applying the rules for cubing exponentials. First, cube the digit term as you normally would, which in this case is 25^3. Next, multiply the exponent of each variable by 3, so the exponents of x and y become 2*3 and 14*3 respectively. As a result, the expression simplifies to 15625x^6y^{42}.
To find the value of the exponential expression (25x^2y^14)^3, we need to cube each term inside the parentheses. The value of (25x^2y^14)^3 is equal to (25^3) * (x^2)^3 * (y^14)^3.
By applying the rule of cubing exponentials, the simplified expression becomes 15625x^6y^42.
Therefore, the value of the given exponential expression is 15625x^6y^42.