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Answer :
To solve the problem step-by-step, let's start by finding the value of [tex]\( m \)[/tex] from the equation [tex]\( 5^m = 3125 \)[/tex].
1. Find [tex]\( m \)[/tex]:
You know that [tex]\( 5^m = 3125 \)[/tex]. To find [tex]\( m \)[/tex], you need to determine the power to which 5 must be raised to get 3125. Since we know that [tex]\( 5^5 = 3125 \)[/tex], we can see that [tex]\( m = 5 \)[/tex].
2. Calculate [tex]\( 4^{(m-2)} \)[/tex]:
Now that we know [tex]\( m = 5 \)[/tex], we need to find the value of [tex]\( 4^{(m-2)} \)[/tex].
Substitute [tex]\( m = 5 \)[/tex] into the expression for the exponent:
[tex]\[
m - 2 = 5 - 2 = 3
\][/tex]
Therefore, we need to calculate [tex]\( 4^3 \)[/tex].
3. Find [tex]\( 4^3 \)[/tex]:
Calculate [tex]\( 4^3 \)[/tex] using basic exponentiation:
[tex]\[
4^3 = 4 \times 4 \times 4 = 16 \times 4 = 64
\][/tex]
So, the value of [tex]\( 4^{(m-2)} \)[/tex] is 64.
1. Find [tex]\( m \)[/tex]:
You know that [tex]\( 5^m = 3125 \)[/tex]. To find [tex]\( m \)[/tex], you need to determine the power to which 5 must be raised to get 3125. Since we know that [tex]\( 5^5 = 3125 \)[/tex], we can see that [tex]\( m = 5 \)[/tex].
2. Calculate [tex]\( 4^{(m-2)} \)[/tex]:
Now that we know [tex]\( m = 5 \)[/tex], we need to find the value of [tex]\( 4^{(m-2)} \)[/tex].
Substitute [tex]\( m = 5 \)[/tex] into the expression for the exponent:
[tex]\[
m - 2 = 5 - 2 = 3
\][/tex]
Therefore, we need to calculate [tex]\( 4^3 \)[/tex].
3. Find [tex]\( 4^3 \)[/tex]:
Calculate [tex]\( 4^3 \)[/tex] using basic exponentiation:
[tex]\[
4^3 = 4 \times 4 \times 4 = 16 \times 4 = 64
\][/tex]
So, the value of [tex]\( 4^{(m-2)} \)[/tex] is 64.
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