Of course! Let's solve the problem step-by-step.
We want to express the sum of four terms of [tex]\(4^2\)[/tex] as a single power of 4. Here is how to do that:
1. Understand the initial expression:
The given expression is [tex]\(4^2 + 4^2 + 4^2 + 4^2\)[/tex].
2. Combine like terms:
Since there are four identical terms of [tex]\(4^2\)[/tex], we can factor out [tex]\(4^2\)[/tex] as follows:
[tex]\[
4^2 + 4^2 + 4^2 + 4^2 = 4 \times 4^2
\][/tex]
3. Use properties of exponents:
Recall that [tex]\(4^1 = 4\)[/tex]. So we can rewrite the expression [tex]\(4 \times 4^2\)[/tex] using exponent rules. Specifically, [tex]\(a^m \times a^n = a^{m+n}\)[/tex].
[tex]\[
4 \times 4^2 = 4^1 \times 4^2
\][/tex]
4. Combine the exponents:
According to the rules of exponents [tex]\((a^m \times a^n = a^{m+n})\)[/tex],
[tex]\[
4^1 \times 4^2 = 4^{1+2}
\][/tex]
Simplifying the exponent,
[tex]\[
4^{1+2} = 4^3
\][/tex]
Therefore, the expression [tex]\(4^2 + 4^2 + 4^2 + 4^2\)[/tex] can be expressed as [tex]\(4^3\)[/tex].
Thus, the correct answer is:
d. [tex]\(4^3\)[/tex]
