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If [tex]$5^a = 3125$[/tex], the value of [tex]$5^{(a-3)}$[/tex] is:

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.

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