Answer
$393.4 \text{ million}$
Work Step by Step
Since $2015$ is $20$ years after $1995,$ then $x=20.$
Substituting $x=20$ in the given function, $
f(x)=25x^{23/25}
,$ then
\begin{array}{l}\require{cancel}
f(x)=25(20)^{23/25}
.\end{array}
Using the definition of rational exponents which is given by $a^{\frac{m}{n}}=\sqrt[n]{a^m}=\left(\sqrt[n]{a}\right)^m,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
f(x)=25\sqrt[25]{20^{23}}
.\end{array}
Using the laws of exponents and the properties of radicals, the expression above is equivalent to
\begin{array}{l}\require{cancel}
f(x)=25\sqrt[25]{(2^2\cdot5)^{23}}
\\
f(x)=25\sqrt[25]{2^{2(23)}\cdot5^{23}}
\\
f(x)=25\sqrt[25]{2^{46}\cdot5^{23}}
\\
f(x)=25\sqrt[25]{2^{25}\cdot2^{21}\cdot5^{23}}
\\
f(x)=25(2)\sqrt[25]{2^{21}\cdot5^{23}}
\\
f(x)=50\sqrt[25]{2^{21}\cdot5^{23}}
\\
f(x)=50\sqrt[25]{2^{21}\cdot5^{21}\cdot5^2}
\\
f(x)=50\sqrt[25]{(2\cdot5)^{21}\cdot5^2}
\\
f(x)=50\sqrt[25]{10^{21}\cdot25}
\\
f(x)\approx393.4
.\end{array}
Hence, the number of cellular subscriptions, $f(x),$ is $
393.4 \text{ million}
.$
