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------------------------------------------------ Which expression is equivalent to [tex]2.5^2 - 3y[/tex]?

A. [tex]\frac{6.25}{(15.625)^{-y}}[/tex]
B. [tex]6.25(2.5)^{3y}[/tex]
C. [tex]6.25 - (2.5)^{3y}[/tex]
D. [tex]6.25(15.625)^{-y}[/tex]

Answer :

To determine which expression is equivalent to [tex]\(2.5^2 - 3y\)[/tex], let's go through each option step by step.

1. Simplify the expression [tex]\(2.5^2 - 3y\)[/tex]:

- [tex]\(2.5^2 = 6.25\)[/tex].
- Therefore, the expression simplifies to [tex]\(6.25 - 3y\)[/tex].

Let's compare the simplified expression with each option:

2. Option (a): [tex]\(\frac{6.25}{(15,625)^{-y}}\)[/tex]

- This can be expressed as [tex]\(6.25 \times (15,625)^y\)[/tex].
- This does not match the form [tex]\(6.25 - 3y\)[/tex].

3. Option (b): [tex]\(6.25(2.5)^{3y}\)[/tex]

- This can be written as [tex]\(6.25 \times (2.5^3)^y\)[/tex].
- This is not comparable to [tex]\(6.25 - 3y\)[/tex].

4. Option (c): [tex]\(6.25 - (2.5)^{3y}\)[/tex]

- This subtracts the expression [tex]\((2.5)^{3y}\)[/tex] from 6.25.
- This form does not match [tex]\(6.25 - 3y\)[/tex].

5. Option (d): [tex]\(6.25(15,625)^{-y}\)[/tex]

- This is equivalent to [tex]\(6.25 / (15,625)^y\)[/tex].
- This form does not align with [tex]\(6.25 - 3y\)[/tex].

6. Option (e): [tex]\(\frac{6.25}{(15,625) - y}\)[/tex]

- This expression can be seen as [tex]\(\frac{6.25}{15,625} - y\)[/tex].
- It does not match the form of [tex]\(6.25 - 3y\)[/tex].

Upon reviewing all options, none of them is equivalent to [tex]\(6.25 - 3y\)[/tex]. Therefore, the answer is that none of the given options is equivalent to the expression [tex]\(2.5^2 - 3y\)[/tex].