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Answer :
To find an expression equivalent to [tex]\(2.5^{2-3y}\)[/tex], we need to use the properties of exponents. Here’s a step-by-step breakdown:
1. Understand the Given Expression:
We have the expression [tex]\(2.5^{2 - 3y}\)[/tex].
2. Apply Exponent Rules:
According to the exponent rule [tex]\(a^{b-c} = \frac{a^b}{a^c}\)[/tex], the expression [tex]\(2.5^{2 - 3y}\)[/tex] can be rewritten as:
[tex]\[
\frac{2.5^2}{(2.5)^{3y}}
\][/tex]
3. Calculate [tex]\(2.5^2\)[/tex]:
First, compute [tex]\(2.5^2\)[/tex]:
[tex]\[
2.5 \times 2.5 = 6.25
\][/tex]
So, [tex]\(2.5^2 = 6.25\)[/tex].
4. Express the Denominator Using Exponent Properties:
Notice that [tex]\((2.5)^{3y}\)[/tex] can also be expressed using powers of another number. We can find that [tex]\(2.5^3 = 15.625\)[/tex], so:
[tex]\[
(2.5)^{3y} = (15.625)^y
\][/tex]
5. Rewrite Using Negative Exponent:
The expression [tex]\(\frac{2.5^2}{(2.5)^{3y}}\)[/tex] can now be written as:
[tex]\[
6.25 \times (15.625)^{-y}
\][/tex]
By following these steps and calculations, we determine that the expression equivalent to [tex]\(2.5^{2-3y}\)[/tex] is [tex]\(6.25(15.625)^{-y}\)[/tex].
Therefore, the correct choice is:
[tex]\[
6.25(15.625)^{-y}
\][/tex]
1. Understand the Given Expression:
We have the expression [tex]\(2.5^{2 - 3y}\)[/tex].
2. Apply Exponent Rules:
According to the exponent rule [tex]\(a^{b-c} = \frac{a^b}{a^c}\)[/tex], the expression [tex]\(2.5^{2 - 3y}\)[/tex] can be rewritten as:
[tex]\[
\frac{2.5^2}{(2.5)^{3y}}
\][/tex]
3. Calculate [tex]\(2.5^2\)[/tex]:
First, compute [tex]\(2.5^2\)[/tex]:
[tex]\[
2.5 \times 2.5 = 6.25
\][/tex]
So, [tex]\(2.5^2 = 6.25\)[/tex].
4. Express the Denominator Using Exponent Properties:
Notice that [tex]\((2.5)^{3y}\)[/tex] can also be expressed using powers of another number. We can find that [tex]\(2.5^3 = 15.625\)[/tex], so:
[tex]\[
(2.5)^{3y} = (15.625)^y
\][/tex]
5. Rewrite Using Negative Exponent:
The expression [tex]\(\frac{2.5^2}{(2.5)^{3y}}\)[/tex] can now be written as:
[tex]\[
6.25 \times (15.625)^{-y}
\][/tex]
By following these steps and calculations, we determine that the expression equivalent to [tex]\(2.5^{2-3y}\)[/tex] is [tex]\(6.25(15.625)^{-y}\)[/tex].
Therefore, the correct choice is:
[tex]\[
6.25(15.625)^{-y}
\][/tex]
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