Answer
\[1.2\times {{10}^{1}}\].
Work Step by Step
If a number is expressed as \[a\times {{10}^{n}}\], where a is a number greater than or equal to 1 and less than 10, and n is an integer, then the number is said to be expressed in scientific notation.
Hence all the four numbers, \[1.2\times {{10}^{6}}\], \[8.7\times {{10}^{-2}}\], \[2.9\times {{10}^{6}}\] and \[3\times {{10}^{-3}}\], involved in the given expression are expressed in scientific notation.
Now, to compute the given expression, break the computation into three parts. First, compute the multiplications \[\left( 1.2\times {{10}^{6}} \right)\left( 8.7\times {{10}^{-2}} \right)\] and \[\left( 2.9\times {{10}^{6}} \right)\left( 3\times {{10}^{-3}} \right)\] separately, and then divide the result of the first multiplication \[\left( 1.2\times {{10}^{6}} \right)\left( 8.7\times {{10}^{-2}} \right)\] by the result of the second multiplication \[\left( 2.9\times {{10}^{6}} \right)\left( 3\times {{10}^{-3}} \right)\].
Then, perform the multiplication \[\left( a\times b \right)\] as the usual multiplication of any two numbers is performed and the multiplication \[\left( {{10}^{x}}\times {{10}^{y}} \right)\] using the product rule for exponents, explained below. And then write the two results obtained after performing the above two multiplications, together, with the symbol \[\times \] between them.
Now, apply the procedure mentioned above and the product rule for exponents to compute the required multiplications:
\[\begin{align}
& \left( 1.2\times {{10}^{6}} \right)\left( 8.7\times {{10}^{-2}} \right)=\left( 1.2\times 8.7 \right)\left( {{10}^{6}}\times {{10}^{-2}} \right) \\
& =\left( 10.44 \right)\left( {{10}^{6-2}} \right) \\
& =10.44\times {{10}^{4}}
\end{align}\]
Hence, \[\left( 1.2\times {{10}^{6}} \right)\left( 8.7\times {{10}^{-2}} \right)=10.44\times {{10}^{4}}\].
Similarly,
\[\begin{align}
& \left( 2.9\times {{10}^{6}} \right)\left( 3\times {{10}^{-3}} \right)=\left( 2.9\times 3 \right)\left( {{10}^{6}}\times {{10}^{-3}} \right) \\
& =\left( 8.7 \right)\left( {{10}^{6-3}} \right) \\
& =8.7\times {{10}^{3}}
\end{align}\]
Hence, \[\left( 2.9\times {{10}^{6}} \right)\left( 3\times {{10}^{-3}} \right)=8.7\times {{10}^{3}}\].
Now, divide the result of the first multiplication \[\left( 1.2\times {{10}^{6}} \right)\left( 8.7\times {{10}^{-2}} \right)\] by the result of the second multiplication \[\left( 2.9\times {{10}^{6}} \right)\left( 3\times {{10}^{-3}} \right)\]:
\[\frac{\left( 1.2\times {{10}^{6}} \right)\left( 8.7\times {{10}^{-2}} \right)}{\left( 2.9\times {{10}^{6}} \right)\left( 3\times {{10}^{-3}} \right)}=\frac{10.44\times {{10}^{4}}}{8.7\times {{10}^{3}}}\]
Then, perform the division \[\left( \frac{a}{b} \right)\] as the usual division of any two numbers is performed and the division \[\left( \frac{{{10}^{x}}}{{{10}^{y}}} \right)\] using the quotient rule for exponents, explained below. And then write the two results obtained after performing the above two divisions, together, with the symbol \[\times \] between them.
Now, apply the procedure mentioned above and the quotient rule for exponents to compute the required division:
\[\begin{align}
& \frac{10.44\times {{10}^{4}}}{8.7\times {{10}^{3}}}=\left( \frac{10.44}{8.7} \right)\times \left( \frac{{{10}^{4}}}{{{10}^{3}}} \right) \\
& =\left( \frac{\left( 1.2 \right)\left( \right)}{} \right)\times \left( {{10}^{4-3}} \right) \\
& =1.2\times {{10}^{1}}
\end{align}\]
Hence,
\[\begin{align}
& \frac{\left( 1.2\times {{10}^{6}} \right)\left( 8.7\times {{10}^{-2}} \right)}{\left( 2.9\times {{10}^{6}} \right)\left( 3\times {{10}^{-3}} \right)}=\frac{10.44\times {{10}^{4}}}{8.7\times {{10}^{3}}} \\
& =1.2\times {{10}^{1}}
\end{align}\]
