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Answer :
Sure, let's solve this step by step!
We are given the equation [tex]\(5^m = 3125\)[/tex]. Our goal is to find the value of [tex]\(4^{(m-2)}\)[/tex].
Step 1: Solve for [tex]\(m\)[/tex] in the equation [tex]\(5^m = 3125\)[/tex].
- Notice that 3125 is a power of 5. We need to determine which power of 5 equals 3125.
- By evaluating, we find:
- [tex]\(5^1 = 5\)[/tex]
- [tex]\(5^2 = 25\)[/tex]
- [tex]\(5^3 = 125\)[/tex]
- [tex]\(5^4 = 625\)[/tex]
- [tex]\(5^5 = 3125\)[/tex]
So, [tex]\(m = 5\)[/tex].
Step 2: Substitute [tex]\(m = 5\)[/tex] into [tex]\(4^{(m-2)}\)[/tex].
- Since [tex]\(m = 5\)[/tex], we have:
[tex]\[
m - 2 = 5 - 2 = 3
\][/tex]
- Now, calculate [tex]\(4^3\)[/tex]:
[tex]\[
4^3 = 4 \times 4 \times 4 = 16 \times 4 = 64
\][/tex]
Thus, the value of [tex]\(4^{(m-2)}\)[/tex] is [tex]\(64\)[/tex].
Therefore, the final answer is 64.
We are given the equation [tex]\(5^m = 3125\)[/tex]. Our goal is to find the value of [tex]\(4^{(m-2)}\)[/tex].
Step 1: Solve for [tex]\(m\)[/tex] in the equation [tex]\(5^m = 3125\)[/tex].
- Notice that 3125 is a power of 5. We need to determine which power of 5 equals 3125.
- By evaluating, we find:
- [tex]\(5^1 = 5\)[/tex]
- [tex]\(5^2 = 25\)[/tex]
- [tex]\(5^3 = 125\)[/tex]
- [tex]\(5^4 = 625\)[/tex]
- [tex]\(5^5 = 3125\)[/tex]
So, [tex]\(m = 5\)[/tex].
Step 2: Substitute [tex]\(m = 5\)[/tex] into [tex]\(4^{(m-2)}\)[/tex].
- Since [tex]\(m = 5\)[/tex], we have:
[tex]\[
m - 2 = 5 - 2 = 3
\][/tex]
- Now, calculate [tex]\(4^3\)[/tex]:
[tex]\[
4^3 = 4 \times 4 \times 4 = 16 \times 4 = 64
\][/tex]
Thus, the value of [tex]\(4^{(m-2)}\)[/tex] is [tex]\(64\)[/tex].
Therefore, the final answer is 64.
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