Answer
$\text{Scientific notation: }
3.0\times10^{-4}
\\\text{Standard form: }
0.0003$
Work Step by Step
A number in scientific notation takes the form $a\times10^n$ where $1\le a\lt10$ and $n$ is an integer. Hence, the given expression, $
\dfrac{2,500,000\times0.00003}{0.05\times5,000,000}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{(2.5\times10^6)(3.0\times10^{-5})}{(5.0\times10^{-2})(5.0\times10^{6})}
.\end{array}
Using the law of exponents which states that $a^x\cdot a^y=a^{x+y},$ the expression above simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(2.5)(3.0)\times10^{6+(-5)}}{(5.0)(5.0)\times10^{-2+6}}
\\\\=
\dfrac{7.5\times10^{1}}{25\times10^{4}}
.\end{array}
Using the law of exponents which states that $\dfrac{a^x}{a^y}=a^{x-y},$ the expression above simplifies to
\begin{array}{l}\require{cancel}
7.5\div25\times10^{1-4}
\\\\=
0.3\times10^{-3}
\\\\=
0.3\times10^{-3}
.\end{array}
Hence, the simplified form is
\begin{array}{l}\require{cancel}
\text{Scientific notation: }
3.0\times10^{-4}
\\\text{Standard form: }
0.0003
.\end{array}