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Answer :
Sure! Let's solve the problem step-by-step.
We are provided with the equation:
[tex]\[ 5^m = 3125 \][/tex]
Step 1: Find the value of [tex]\( m \)[/tex].
First, we need to express [tex]\( 3125 \)[/tex] as a power of [tex]\( 5 \)[/tex]:
[tex]\[ 3125 = 5^5 \][/tex]
So, we can equate the exponents:
[tex]\[ m = 5 \][/tex]
Step 2: Find the value of [tex]\( 4^{(m-2)} \)[/tex].
Now that we have [tex]\( m = 5 \)[/tex], we substitute [tex]\( m \)[/tex] into the expression [tex]\( 4^{(m-2)} \)[/tex]:
[tex]\[ 4^{(m-2)} = 4^{(5-2)} \][/tex]
[tex]\[ 4^{(5-2)} = 4^3 \][/tex]
Step 3: Calculate [tex]\( 4^3 \)[/tex].
We know that:
[tex]\[ 4^3 = 4 \times 4 \times 4 = 64 \][/tex]
Therefore, the value of [tex]\( 4^{(m-2)} \)[/tex] is:
[tex]\[ 64 \][/tex]
So, the final result is:
[tex]\[ 4^{(m-2)} = 64 \][/tex]
We are provided with the equation:
[tex]\[ 5^m = 3125 \][/tex]
Step 1: Find the value of [tex]\( m \)[/tex].
First, we need to express [tex]\( 3125 \)[/tex] as a power of [tex]\( 5 \)[/tex]:
[tex]\[ 3125 = 5^5 \][/tex]
So, we can equate the exponents:
[tex]\[ m = 5 \][/tex]
Step 2: Find the value of [tex]\( 4^{(m-2)} \)[/tex].
Now that we have [tex]\( m = 5 \)[/tex], we substitute [tex]\( m \)[/tex] into the expression [tex]\( 4^{(m-2)} \)[/tex]:
[tex]\[ 4^{(m-2)} = 4^{(5-2)} \][/tex]
[tex]\[ 4^{(5-2)} = 4^3 \][/tex]
Step 3: Calculate [tex]\( 4^3 \)[/tex].
We know that:
[tex]\[ 4^3 = 4 \times 4 \times 4 = 64 \][/tex]
Therefore, the value of [tex]\( 4^{(m-2)} \)[/tex] is:
[tex]\[ 64 \][/tex]
So, the final result is:
[tex]\[ 4^{(m-2)} = 64 \][/tex]
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