Answer :
To find the expression equivalent to \( 2^{4x - 5} \) among the given options, we need to compare each option by breaking them down into simpler bases similar to \( 2 \).
### Step-by-Step Breakdown:
1. Option 1: \(\frac{8^x}{10}\)
[tex]\[ 8^x = (2^3)^x = 2^{3x} \][/tex]
[tex]\[ \frac{8^x}{10} = \frac{2^{3x}}{10} \][/tex]
This does not match the form \( 2^{4x - 5} \).
2. Option 2: \(\frac{4^x}{5}\)
[tex]\[ 4^x = (2^2)^x = 2^{2x} \][/tex]
[tex]\[ \frac{4^x}{5} = \frac{2^{2x}}{5} \][/tex]
This also does not match the form \( 2^{4x - 5} \).
3. Option 3: \(\frac{16^x}{32}\)
[tex]\[ 16^x = (2^4)^x = 2^{4x} \][/tex]
[tex]\[ 32 = 2^5 \][/tex]
[tex]\[ \frac{16^x}{32} = \frac{2^{4x}}{2^5} = 2^{4x - 5} \][/tex]
This matches the form \( 2^{4x - 5} \).
4. Option 4: \(\frac{1^x}{32}\)
[tex]\[ 1^x = 1 \][/tex]
[tex]\[ \frac{1^x}{32} = \frac{1}{32} = \frac{1}{2^5} \][/tex]
This does not match the form \( 2^{4x - 5} \).
### Conclusion:
The expression [tex]\(\frac{16^x}{32}\)[/tex] simplifies to [tex]\( 2^{4x - 5} \)[/tex]. Therefore, the equivalent expression to [tex]\( 2^{4x - 5} \)[/tex] is [tex]\(\boxed{\frac{16^x}{32}}\)[/tex].
### Step-by-Step Breakdown:
1. Option 1: \(\frac{8^x}{10}\)
[tex]\[ 8^x = (2^3)^x = 2^{3x} \][/tex]
[tex]\[ \frac{8^x}{10} = \frac{2^{3x}}{10} \][/tex]
This does not match the form \( 2^{4x - 5} \).
2. Option 2: \(\frac{4^x}{5}\)
[tex]\[ 4^x = (2^2)^x = 2^{2x} \][/tex]
[tex]\[ \frac{4^x}{5} = \frac{2^{2x}}{5} \][/tex]
This also does not match the form \( 2^{4x - 5} \).
3. Option 3: \(\frac{16^x}{32}\)
[tex]\[ 16^x = (2^4)^x = 2^{4x} \][/tex]
[tex]\[ 32 = 2^5 \][/tex]
[tex]\[ \frac{16^x}{32} = \frac{2^{4x}}{2^5} = 2^{4x - 5} \][/tex]
This matches the form \( 2^{4x - 5} \).
4. Option 4: \(\frac{1^x}{32}\)
[tex]\[ 1^x = 1 \][/tex]
[tex]\[ \frac{1^x}{32} = \frac{1}{32} = \frac{1}{2^5} \][/tex]
This does not match the form \( 2^{4x - 5} \).
### Conclusion:
The expression [tex]\(\frac{16^x}{32}\)[/tex] simplifies to [tex]\( 2^{4x - 5} \)[/tex]. Therefore, the equivalent expression to [tex]\( 2^{4x - 5} \)[/tex] is [tex]\(\boxed{\frac{16^x}{32}}\)[/tex].
