Question

1. $(3.7 \times 10^{4}) \times (9.1 \times 10^{2})$
2. $(-4.4 \times 10^{3}) \times (6.0 \times 10^{9})$
3. $(9.6 \times 10^{-5}) \times (7.1 \times 10^{-4})$
4. $(5.8 \times 10^{8}) \times (3.5 \times 10^{-3})$

Explanation:

Problem 1: \((3.7 \times 10^{4}) \times (9.1 \times 10^{2})\)

Step 1: Multiply the coefficients

Multiply \(3.7\) and \(9.1\).
\(3.7\times9.1 = 33.67\)

Step 2: Add the exponents of 10

Using the rule \(a^m\times a^n=a^{m + n}\), for \(10^{4}\times10^{2}\), we have \(10^{4+2}=10^{6}\)

Step 3: Combine the results

Multiply the result from step 1 and step 2: \(33.67\times10^{6}\)

Step 4: Convert to proper scientific notation

We need to have one non - zero digit before the decimal point. So, \(33.67\times10^{6}=3.367\times10^{7}\)

Step 1: Multiply the coefficients

Multiply \(-4.4\) and \(6.0\).
\(-4.4\times6.0=-26.4\)

Step 2: Add the exponents of 10

Using the rule \(a^m\times a^n = a^{m + n}\), for \(10^{3}\times10^{9}\), we have \(10^{3 + 9}=10^{12}\)

Step 3: Combine the results

Multiply the result from step 1 and step 2: \(-26.4\times10^{12}\)

Step 4: Convert to proper scientific notation

\(-26.4\times10^{12}=-2.64\times10^{13}\)

Step 1: Multiply the coefficients

Multiply \(9.6\) and \(7.1\).
\(9.6\times7.1 = 68.16\)

Step 2: Add the exponents of 10

Using the rule \(a^m\times a^n=a^{m + n}\), for \(10^{-5}\times10^{-4}\), we have \(10^{-5+( - 4)}=10^{-9}\)

Step 3: Combine the results

Multiply the result from step 1 and step 2: \(68.16\times10^{-9}\)

Step 4: Convert to proper scientific notation

\(68.16\times10^{-9}=6.816\times10^{-8}\)

Answer:

\(3.367\times 10^{7}\)

Problem 2: \((- 4.4\times10^{3})\times(6.0\times10^{9})\)