NCERT Solutions for Chapter: Exponents and Powers, Exercise 1: Exercise

 Astronomy table shows the mass of the planets, the sun and the moon in our solar system.

Which planet has about the same mass as earth$?$

While studying her family's history. Shikha discovers records of ancestors $12$ generations back. She wonders how many ancestors she has had in the past $12$generations. She starts to make a diagram to help her figure this out. The diagram soon becomes very complex.

Write an equation for the number of ancestors in a given generation $\mathrm{n}$.

Repeater machine is a hypothetical machine which automatically enlarges items several times. For example, sending a piece of wire through

$a\left(\times 2^4\right)$ machine is the same as putting it through a $(\times 2)$ machine four times. So, if you send a $3 \mathrm{cm}$ piece of wire through a $\left(\times 2^4\right)$ machine, its length

becomes $3\times 2\times 2\times 2\times 2=48 \mathrm{cm}$. It can also be written that a base $\left(2\right)$ machine is being applied $4$ times.

What will be the new length of a $4 \mathrm{cm}$ strip inserted in the machine?

Supply the missing information for each diagram.

Mass of Mars is $6.42\times {10}^{29} \mathrm{kg}$ and mass of the Sun is $1.99\times {10}^{30} \mathrm{kg}$. What is the total mass?

The distance between the Sun and the Earth is $1.496\times {10}^8 \mathrm{km}$ and distance between the Earth and the Moon is $3.84\times {10}^8 \mathrm{m}$. During solar eclipse the Moon comes in between the Earth and the Sun. What is distance between the Moon and the Sun at that particular time?

A particular star is at a distance of about $8.1\times {10}^{13} \mathrm{km}$ from the Earth. Assuring that light travels at $3\times {10}^8 \mathrm{m}$ per second, find how long does light take from that star to reach the Earth.

By what number should $(-8{)}^{-3}$ be multiplied so that the product may be equal to $(-6{)}^{-3}$?