Vistor Chow wal keung and RC Yadav Solutions for Chapter: Powers and Exponents, Exercise 3: REVIEW EXERCISE

Simplify the following and express your answer using a positive exponent.

${\left(3{\mathrm{p}}^{-3}{\mathrm{q}}^{-1}\right)}^2{\left(-4{\mathrm{p}}^3{\mathrm{q}}^{-2}\right)}^2$

Simplify the following and express your answer using positive exponent.

$\frac{{\left({\mathrm{r}}^{-3}{\mathrm{s}}^{-4}\right)}^{-3}}{{\left({\mathrm{r}}^{-2}{\mathrm{s}}^{-5}\right)}^{-6}}$

Simplify the following and express your answer using a positive exponent.

${\left({\mathrm{x}}^{-2}\mathrm{y}\right)}^{-5}\times {\left(\frac{{\mathrm{x}}^3}{{\mathrm{y}}^2}\right)}^{-4}$

The total amount of drug introduced into the body with ${\mathrm{a}}^5{\mathrm{c}}^{-1}$ cells from an injection is ${\mathrm{a}}^9{\mathrm{c}}^{-3}$ units. Find the average amount of drug per cell, expressing your answer using positive exponents.

The equatorial radius of the Earth is the distance from the centre of the Earth to the equator. It is about $6378.5 \mathrm{km}$. Find the equatorial radius in metres, expressing your answer in scientific notation.

The speed of light in air is $3\times {10}^8 \mathrm{m}/\mathrm{s}$. Find the time taken for a light beam to travel a distance equal to the equatorial radius. Give your answer correct to three decimal places.

Show with examples how the scientific notation is more effective in writing extremely large or small numbers.

In what way does the scientific notation help you to understand why our number system is called a base $10$ system?