Verified Answer :

RedRicin

\(f(x)=4(7)^{2x}\)

Let's look at the way each of these attempts to simplify our expression.

Answer A simply mulltiplies the 4 and the 7 to get 28. This is the correct answer.

The reason you can't just do squaring (to the power of 2) and then go to the power of x later is because you would write that as \(n^{2^x}\), not \(n^{2x}\).

Answer:

Option: B is correct. (\(f(x)=4\times (49)^x\))

Step-by-step explanation:

We are asked to find which expression is equivalent to the mathematical expression:

\(f(x)=4(7)^{2x}\)

We know that any expression of the kind \(a^{mn}\) could also be represented as \((a^m)^n\)

Hence on converting the given expression using the above representation we have:

\(f(x)=4\times (7)^{2x}=4\times (7^2)^x=4\times (49)^x\)

Hence f(x) could also be written as:

\(f(x)=4\times (49)^x\)

Hence, option B is correct.


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