Final answer:
The value of the monomial 24x^4 depends on the given value for the variable x. It is calculated by replacing x with the given value and raising the result to the fourth power. Without a specific value for x, the monomial remains unevaluated.
Step-by-step explanation:
The student is asking to evaluate a monomial, which in this case is 24x^4, given the values of the variable. To do this, we replace x with the given value and then raise the entire expression to the fourth power. If a specific value for x is not given, we cannot complete the evaluation; in that case, the expression remains as an algebraic expression representing what would be the result were a value for x supplied.
Raising a monomial like 24x^4 to a power means multiplying the base, which is 24x, by itself the number of times indicated by the exponent, which is 4 in this case. If we had a value for x, say 2, we would calculate it as follows: (24*2)^4, first multiplying 24 by 2, and then raising the result to the fourth power. Remember that exponents only affect the components inside the parentheses.
Lastly, it's important to understand the general principle for raising numbers to powers. For instance, an expression like n^x equates to n multiplied by itself x-1 times. For the student's question, without a specific value for x, the monomial remains unevaluated, but the process of evaluation is clear.
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