Question

Use the scientific notation, the Laws of exponents, and a calculator to perform the indicated operations. State your answer rounded to the number of significant digits indicated by the given data.

$\frac{\left(73.1\right)\left(1.6341\right)\times {10}^{28}}{0.0000000019}$

Short answer

The required answer is $6.286984\times {10}^{38}$.

Step-by-step solution

Step 1. Scientific Notation and exponent rule.

A positive number x is said to be written in scientific notation if it is expressed as follows:

$x=a\times {10}^n\text{where}1\le a<10$ and n is an integer.

Multiplication rule: $a^m{a}^n=a^{m+n}$

Division rule: $\frac{a^m}{a^n}=a^{m-n}$

Step 2. Perform multiplication and division.

Consider the given number$\frac{\left(73.1\right)(1.6341\times {10}^{28})}{0.0000000019}$

Rewrite the denominator into scientific notation.

$\frac{\left(73.1\right)(1.6341\times {10}^{28})}{1.9\times {10}^{-9}}$

Simplify the number except factor 10.

$\begin{array}{l}\frac{\left(73.1\right)(1.6341\times {10}^{28})}{1.9\times {10}^{-9}}=\frac{119.45271\times {10}^{28}}{1.9\times {10}^{-9}}\\ =\frac{1.1945271\times {10}^{30}}{1.9\times {10}^{-9}}\\ \approx \frac{0.6286984\times {10}^{30}}{1\times {10}^{-9}}\end{array}$

Step 3. Use exponent and Scientific Notation rule.

$\begin{array}{l}\frac{\left(73.1\right)(1.6341\times {10}^{28})}{1.9\times {10}^{-9}}=\frac{0.6286984\times {10}^{30}}{1\times {10}^{-9}}\\ =0.6286984\times {10}^{30-(-9)}\\ =0.6286984\times {10}^{39}\\ =6.286984\times {10}^{38}\end{array}$