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

Answer :

To solve the problem, we start with the given equation:

[tex]\( 5^a = 3125 \)[/tex].

We need to find [tex]\( 5^{(a-3)} \)[/tex].

### Step 1: Find the value of [tex]\( a \)[/tex]

Since [tex]\( 5^a = 3125 \)[/tex], we can express 3125 using powers of 5. Notice that:
[tex]\[ 3125 = 5 \times 5 \times 5 \times 5 \times 5 = 5^5 \][/tex]

Thus, [tex]\( a = 5 \)[/tex].

### Step 2: Calculate [tex]\( 5^{(a-3)} \)[/tex]

Now that we know [tex]\( a = 5 \)[/tex], substitute [tex]\( a-3 \)[/tex] into the expression:

[tex]\[ 5^{(a-3)} = 5^{(5-3)} = 5^2 \][/tex]

### Step 3: Simplify [tex]\( 5^2 \)[/tex]

Finally, calculate [tex]\( 5^2 \)[/tex]:
[tex]\[ 5^2 = 25 \][/tex]

Therefore, the value of [tex]\( 5^{(a-3)} \)[/tex] is [tex]\( 25 \)[/tex].

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