Embibe Experts Solutions for Chapter: Exponents and Powers, Exercise 1: Exercise

The atomic number of a carbon atom is $6$. The number of protons and electrons in a carbon atom is $6.$ The weight of a proton is $\approx$$1.67492\times {10}^{-27} \mathrm{kg}$  and that of an electron is $\approx 9.1\times {10}^{-31} \mathrm{kg}$. Find the product of the weight of all the protons and electrons in the carbon atom.

The galaxy that includes our Solar System, Milky Way, is approximately $9.5\times {10}^{17} \mathrm{km}$ in diameter. The Indian Space Research Organisation has developed the fastest spacecraft in the world, named Sansara, which can travel with a speed of $190 \mathrm{km}/\mathrm{s}$.  Find the time taken by the spacecraft to travel the whole diameter of the Milky Way.

If an average mosquito typically weighs around $5 \mathrm{mg}$ and an elephant weighs around $4000 \mathrm{kg}$, then how many mosquitos does it take to weigh as much as an elephant?

The mathematics teacher of class $8$ taught a new topic, A perfect cube, which is a number,obtained by multiplying the same integer three times or we can rewrite the expression as $a^3$, where $a$ is a whole number. The teacher bought with her a box which consist of four numbers. One of the numbers is a perfect cube. Help the students to identify the perfect cube.

In today's class, the Mathematics teacher bought with him a box full of numbers, where the numbers are of the form $x^y$, where $0<x<1$. The numbers in the box are $x^1, x^{-1}, x^{-2}$ and $x^{-3}$. Arrange the numbers in correct order.

If an average ant weighs$2\times {10}^{-6} \mathrm{kg}$ and there are around $10$ quintillion $={10}^{17}$ ants in the world. If a human weighs $50 \mathrm{kg}$ and there are $8,000,000,000$humans, then find the ratio of total weight of humans to the total weight of ants.

In a chart, the masses of four planets of our Solar System are mentioned as given below:

Mercury: $3.3\times {10}^{23} \mathrm{kg}$

Venus: $4.87\times {10}^{24} \mathrm{kg}$

Earth: $5.97\times {10}^{24} \mathrm{kg}$

Mars: $6.4\times {10}^{23} \mathrm{kg}$

If the Sun's mass is known to be $1.989\times {10}^{30} \mathrm{kg}$, then how many combinations of Mercury, Venus, Earth and Mars can fit into one Sun? (Round off to the nearest whole number)

The exponent refers to the number of times a number is multiplied by itself. E.g. $\underset{n \mathrm{times}}{\underbrace{a\times a\times a\times ......\times a}}=a^n$.

Find $1^{2^{3^{4^{5^{6^{7^8}}}}}}$.