Chapter 9, Problem 39SGR

To determine

To calculate: To find how many times farther from the Sun is Saturn than Venus

Answer to Problem 39SGR

Saturn is $10$ times farther from Sun than Venus.

Explanation of Solution

Given information: Venus is about ${10}^8$ kilometers from the Sun and Saturn is about ${10}^9$ kilometers from the Sun

Formula Used:

Exponential identities are

  $x^a{x}^b=x^{a+b}$

  $x^a{y}^a={\left(xy\right)}^a$

  ${\left(x^a\right)}^b={\left(x\right)}^{ab}$

  $\frac{x^a}{x^b}={\left(x\right)}^{a-b}$

Calculation:

Given that Venus is about ${10}^8$ kilometers from the Sun and Saturn is about ${10}^9$ kilometers from the Sun

Now, expression to find how many times farther from the Sun is Saturn than Venus

  $\frac{{10}^9}{{10}^8}$

On solving the above expression using the exponential identity $\frac{x^a}{x^b}={\left(x\right)}^{a-b}$

  $\begin{array}{l}\frac{{10}^9}{{10}^8}={10}^{9-8}\\ \frac{{10}^9}{{10}^8}={10}^1\\ \frac{{10}^9}{{10}^8}=10\end{array}$

Conclusion:

Hence, Saturn is $10$ times farther from Sun than Venus.