Answer :
To find an expression equivalent to [tex]\(2.5^{2-3y}\)[/tex], we can simplify the expression step by step. Here's how:
1. Understand the Original Expression:
The original expression is [tex]\(2.5^{2 - 3y}\)[/tex].
2. Break it Down:
Notice that the expression can be rewritten using exponent rules. Let's break it down as follows:
- [tex]\(2.5^{2 - 3y} = 2.5^2 \times 2.5^{-3y}\)[/tex]
3. Calculate [tex]\(2.5^2\)[/tex]:
First, calculate [tex]\(2.5^2\)[/tex]:
- [tex]\(2.5^2 = 6.25\)[/tex]
4. Re-express the Original Expression:
Substituting back, we get:
- [tex]\(2.5^{2 - 3y} = 6.25 \times 2.5^{-3y}\)[/tex]
5. Identify the Correct Answer:
By comparing with the given choices:
- The expression becomes [tex]\(6.25 \times (2.5)^{-3y}\)[/tex].
Now, recognize that [tex]\(2.5^{-3y}\)[/tex] can be rewritten in terms of another base. Since [tex]\((2.5)^3 = 15.625\)[/tex], then:
- [tex]\(2.5^{-3y} = (15.625)^{-y}\)[/tex]
6. Correct Choice:
Therefore, the expression simplifies to:
- [tex]\(6.25 \times (15.625)^{-y}\)[/tex]
This matches the choice:
- [tex]\(6.25(15.625)^{-y}\)[/tex]
So, the equivalent expression is [tex]\(6.25(15.625)^{-y}\)[/tex].
1. Understand the Original Expression:
The original expression is [tex]\(2.5^{2 - 3y}\)[/tex].
2. Break it Down:
Notice that the expression can be rewritten using exponent rules. Let's break it down as follows:
- [tex]\(2.5^{2 - 3y} = 2.5^2 \times 2.5^{-3y}\)[/tex]
3. Calculate [tex]\(2.5^2\)[/tex]:
First, calculate [tex]\(2.5^2\)[/tex]:
- [tex]\(2.5^2 = 6.25\)[/tex]
4. Re-express the Original Expression:
Substituting back, we get:
- [tex]\(2.5^{2 - 3y} = 6.25 \times 2.5^{-3y}\)[/tex]
5. Identify the Correct Answer:
By comparing with the given choices:
- The expression becomes [tex]\(6.25 \times (2.5)^{-3y}\)[/tex].
Now, recognize that [tex]\(2.5^{-3y}\)[/tex] can be rewritten in terms of another base. Since [tex]\((2.5)^3 = 15.625\)[/tex], then:
- [tex]\(2.5^{-3y} = (15.625)^{-y}\)[/tex]
6. Correct Choice:
Therefore, the expression simplifies to:
- [tex]\(6.25 \times (15.625)^{-y}\)[/tex]
This matches the choice:
- [tex]\(6.25(15.625)^{-y}\)[/tex]
So, the equivalent expression is [tex]\(6.25(15.625)^{-y}\)[/tex].
