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.

$(1.062\times {10}^{24})(8.61\times {10}^{19})$

Short answer

The required answer is $9.14382\times {10}^{43}$.

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

Step 2. Multiply the number.

Consider the given number$(1.062\times {10}^{24})(8.61\times {10}^{19})$

Simplify multiply the numbers$1.062\text{and}8.61$.

$1.062\times 8.61=9.14382$

Step 3. Use exponent and Scientific Notation rule.

$\begin{array}{l}(1.062\times {10}^{24})(8.61\times {10}^{19})=9.14382\times ({10}^{24}\times {10}^{19})\\ =9.14382\times \left({10}^{24+19}\right)\\ =9.14382\times {10}^{43}\end{array}$