Final answer:
The correct evaluation of the exponential expression 3x(5+4)²−4² is 243x - 16, which does not match any of the provided multiple-choice options.
Step-by-step explanation:
To evaluate the exponential expression 3x(5+4)²−4², we need to follow the order of operations, sometimes known as PEMDAS or BODMAS. This means we deal with any parentheses and exponents first, then move on to multiplication and subtraction as follows:
- Calculate what's inside the parentheses: (5+4) = 9.
- Apply the exponent: 9² = 81.
- Multiply this by 3x: 3x * 81 = 243x.
- Calculate the exponent for 4: 4² = 16.
- Subtract the square of 4 from the product of 3x and 81: 243x - 16.
Since 243x and 16 do not share the same variable, they cannot be simplified further. This means that the correct evaluation of the expression is 243x - 16, which does not match any of the provided options (a. 81x, b. 25x, c. 9x, d. 16x).