To determine if the expression [tex]\(\frac{2}{5^{2+1}}\)[/tex] can be rewritten in the form [tex]\(a b^t\)[/tex], let's go through a step-by-step process.
1. Evaluate the exponent in the denominator:
[tex]\[
2 + 1 = 3
\][/tex]
Therefore, the expression becomes:
[tex]\[
\frac{2}{5^3}
\][/tex]
2. Rewriting the expression with a negative exponent:
[tex]\[
\frac{1}{5^3} = 5^{-3}
\][/tex]
Thus, the original expression can be written as:
[tex]\[
2 \cdot 5^{-3}
\][/tex]
Now, we have the expression [tex]\(2 \cdot 5^{-3}\)[/tex] in the form [tex]\(a b^t\)[/tex].
So, we can identify the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
[tex]\[
a = 2, \quad b = 5, \quad t = -3
\][/tex]
Thus, the expression [tex]\(\frac{2}{5^{2+1}}\)[/tex] can be rewritten in the form [tex]\(a b^t\)[/tex], and we have:
[tex]\[
\begin{array}{l}
a = 2 \\
b = 5
\end{array}
\][/tex]
