Answer :
To solve the problem, we want to find the value of [tex]\(5^{(a-3)}\)[/tex] given that [tex]\(5^a = 3125\)[/tex].
Let's go through the steps:
1. Determine the value of [tex]\(a\)[/tex]:
Since [tex]\(5^a = 3125\)[/tex], we can find [tex]\(a\)[/tex] by expressing 3125 as a power of 5. We know:
[tex]\[
3125 = 5 \times 5 \times 5 \times 5 \times 5 = 5^5
\][/tex]
Hence, [tex]\(a = 5\)[/tex].
2. Find the value of [tex]\(5^{(a-3)}\)[/tex]:
Now that we know [tex]\(a = 5\)[/tex], we can calculate [tex]\(5^{(a-3)}\)[/tex].
[tex]\(a - 3 = 5 - 3 = 2\)[/tex].
So, [tex]\(5^{(a-3)} = 5^2\)[/tex].
3. Calculate [tex]\(5^2\)[/tex]:
[tex]\[
5^2 = 5 \times 5 = 25
\][/tex]
Thus, the value of [tex]\(5^{(a-3)}\)[/tex] is 25.
Let's go through the steps:
1. Determine the value of [tex]\(a\)[/tex]:
Since [tex]\(5^a = 3125\)[/tex], we can find [tex]\(a\)[/tex] by expressing 3125 as a power of 5. We know:
[tex]\[
3125 = 5 \times 5 \times 5 \times 5 \times 5 = 5^5
\][/tex]
Hence, [tex]\(a = 5\)[/tex].
2. Find the value of [tex]\(5^{(a-3)}\)[/tex]:
Now that we know [tex]\(a = 5\)[/tex], we can calculate [tex]\(5^{(a-3)}\)[/tex].
[tex]\(a - 3 = 5 - 3 = 2\)[/tex].
So, [tex]\(5^{(a-3)} = 5^2\)[/tex].
3. Calculate [tex]\(5^2\)[/tex]:
[tex]\[
5^2 = 5 \times 5 = 25
\][/tex]
Thus, the value of [tex]\(5^{(a-3)}\)[/tex] is 25.
