To express [tex]\(24^7\)[/tex] in expanded form, we need to break down the exponentiation into a product of terms. Here is the step-by-step process:
1. Identify the base and the exponent: The base is [tex]\(24\)[/tex] and the exponent is [tex]\(7\)[/tex].
2. Express [tex]\(24^7\)[/tex] as a product of multiples of 24, starting from the highest exponent to the lowest:
- Start with [tex]\(24^7\)[/tex].
- Then, move to the next term, [tex]\(24^6\)[/tex].
- Continue in this manner with [tex]\(24^5\)[/tex], [tex]\(24^4\)[/tex], [tex]\(24^3\)[/tex], [tex]\(24^2\)[/tex], and finally [tex]\(24^1\)[/tex].
3. Combine all these terms into a single expression by multiplying them together:
[tex]\[
24^7 \cdot 24^6 \cdot 24^5 \cdot 24^4 \cdot 24^3 \cdot 24^2 \cdot 24^1
\][/tex]
Thus, the expanded form of [tex]\(24^7\)[/tex] is given by:
[tex]\[ 24^7 \cdot 24^6 \cdot 24^5 \cdot 24^4 \cdot 24^3 \cdot 24^2 \cdot 24^1 \][/tex]
