Answer :
To solve the problem, we need to find which option is equivalent to the expression [tex]\(2.5^2 - 3y\)[/tex].
Let's first evaluate the given expression:
1. Calculate [tex]\(2.5^2\)[/tex]:
[tex]\[
2.5^2 = 6.25
\][/tex]
So, the given expression is [tex]\(6.25 - 3y\)[/tex].
Now, let's evaluate each option to see which one matches [tex]\(6.25 - 3y\)[/tex].
### Option a:
[tex]\[
\frac{6.25}{(15.625)^{-y}}
\][/tex]
This simplifies to:
[tex]\[
6.25 \times (15.625)^y
\][/tex]
This expression does not match our target of [tex]\(6.25 - 3y\)[/tex].
### Option e:
[tex]\[
\frac{6.25}{(15.625) - y}
\][/tex]
This is quite different because it involves a division by [tex]\(15.625 - y\)[/tex] and won't simplify to any form like [tex]\(6.25 - 3y\)[/tex].
### Option b:
[tex]\[
6.25(2.5)^{3y}
\][/tex]
This expression involves raising [tex]\(2.5\)[/tex] to the power of [tex]\(3y\)[/tex], which is quite different from subtracting [tex]\(3y\)[/tex]. So, it does not match.
### Option c:
[tex]\[
6.25 - (2.5)^{3y}
\][/tex]
This option subtracts [tex]\((2.5)^{3y}\)[/tex] instead of subtracting [tex]\(3y\)[/tex], so it doesn't match.
### Option d:
[tex]\[
6.25(15.625)^{-y}
\][/tex]
This can be rewritten as:
[tex]\[
6.25 \times \frac{1}{(15.625)^y}
\][/tex]
This doesn't match [tex]\(6.25 - 3y\)[/tex] because it's multiplicative rather than subtractive.
After evaluating each option, none of them directly correspond to [tex]\(6.25 - 3y\)[/tex]. If options are meant to approximate or be equivalent under certain conditions, more context or information might be needed to clarify these expressions.
Given this analysis, it seems like none of the options directly match the expression [tex]\(6.25 - 3y\)[/tex], which suggests we might need to revisit the problem or check if there's any misunderstanding of options. If any assumptions about powers or further transformation principles were relevant, they would need clarification.
Let's first evaluate the given expression:
1. Calculate [tex]\(2.5^2\)[/tex]:
[tex]\[
2.5^2 = 6.25
\][/tex]
So, the given expression is [tex]\(6.25 - 3y\)[/tex].
Now, let's evaluate each option to see which one matches [tex]\(6.25 - 3y\)[/tex].
### Option a:
[tex]\[
\frac{6.25}{(15.625)^{-y}}
\][/tex]
This simplifies to:
[tex]\[
6.25 \times (15.625)^y
\][/tex]
This expression does not match our target of [tex]\(6.25 - 3y\)[/tex].
### Option e:
[tex]\[
\frac{6.25}{(15.625) - y}
\][/tex]
This is quite different because it involves a division by [tex]\(15.625 - y\)[/tex] and won't simplify to any form like [tex]\(6.25 - 3y\)[/tex].
### Option b:
[tex]\[
6.25(2.5)^{3y}
\][/tex]
This expression involves raising [tex]\(2.5\)[/tex] to the power of [tex]\(3y\)[/tex], which is quite different from subtracting [tex]\(3y\)[/tex]. So, it does not match.
### Option c:
[tex]\[
6.25 - (2.5)^{3y}
\][/tex]
This option subtracts [tex]\((2.5)^{3y}\)[/tex] instead of subtracting [tex]\(3y\)[/tex], so it doesn't match.
### Option d:
[tex]\[
6.25(15.625)^{-y}
\][/tex]
This can be rewritten as:
[tex]\[
6.25 \times \frac{1}{(15.625)^y}
\][/tex]
This doesn't match [tex]\(6.25 - 3y\)[/tex] because it's multiplicative rather than subtractive.
After evaluating each option, none of them directly correspond to [tex]\(6.25 - 3y\)[/tex]. If options are meant to approximate or be equivalent under certain conditions, more context or information might be needed to clarify these expressions.
Given this analysis, it seems like none of the options directly match the expression [tex]\(6.25 - 3y\)[/tex], which suggests we might need to revisit the problem or check if there's any misunderstanding of options. If any assumptions about powers or further transformation principles were relevant, they would need clarification.
