Comparison of Quantities Using Exponents

Q.

Question 173

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

Q.

Find the difference between the largest $3$ digit number and the smallest $2$ digit number.

Q. The speed of light is $3\times {10}^{8}m/s$ and the speed of sound is $3.43\times {10}^{2}m/s$. Then the speed of light is almost _____ times greater than that of sound.

1. ${10}^{10}$
2. ${10}^3$
3. ${10}^8$
4. ${10}^6$

Q.

Arrange in ascending order.

$2^5,3^3,2^3\times 2,(3^3{)}^2,3^5,4^0,2^3\times 3^1$

Q.

You have a small marble of Wolfgang Mozart. It is 10 inches tall and weighs 16 pounds. The original marble statue is 7 feet tall.

If the original statue were 20 feet tall, how much would it weigh?

Q.

Express the given number as a product of the powers of their prime factors.

$2700$

Q.

If $4^x$ = 64, then

1. $2^{2x}=64$

2. 2x = 6

3. x = 3

4. ${10}^x$=10000

Q.

$\frac{d^n}{d{x}^n}(e^{2x}+e^{-2x})=$

1. $(e^{2x}+{(-1)}^n{e}^{-2x})$

2. $2^n(e^{2x}+e^{-2x})$

3. $2^n(e^{2x}+{(-1)}^n{e}^{-2x})$

4. None of these

Q. Question 87:

Express the given information in scientific notation and then arrange them in descending order of their size.

$\begin{array}{ccc}S.N.& NameofthePlanet& Mass\left(inkg\right)\\ 1.& Mercury& 330000000000000000000000\\ 2.& Venus& 4870000000000000000000000\\ 3.& Earth& 5980000000000000000000000\\ 4.& Mars& 642000000000000000000000\\ 5.& Jupiter& 1900000000000000000000000000\\ 6.& Saturn& 569000000000000000000000000\\ 7.& Uranus& 86900000000000000000000000\\ 8.& Neptune& 102000000000000000000000000\\ 9.& Pluto& 13100000000000000000000\end{array}$

Q.

Simplify
$\frac{1}{x+p}+\frac{1}{x+q}+\frac{1}{x+r}+\frac{px}{x^3+p{x}^2}+\frac{qx}{x^3+q{x}^2}+\frac{rx}{x^3+r{x}^2}$

1. $\frac{1}{x+p+q+r}$

2. $\frac{1}{p}+\frac{1}{q}+\frac{1}{r}$

3. $\frac{3}{x}$

4. $\frac{3}{p+q+r}$

Q. The speed of light =$3\times {10}^{8}m/s$
The speed of sound =$3.43\times {10}^{2}m/s$
The speed of light is almost ${10}^6$ times that of sound

1. True
2. False

Q.

Question 67

State whether the following statement is true or false:

For an integer a, $a^3$ is always greater than $a^2$.

Q.

Question 81 (c)

Express each of the following in single exponential form.
$5^2\times 7^2$

Q. Question 4(h)
Express the number appearing in the following statements in standard form:
(h) 60, 230, 000, 000, 000, 000, 000, 000 molecules are contained in a drop of water weighing 1.8 gm.

Q.

Find the sum of the greatest $7$-digit number and the smallest $5$-digit number.

Q.

Express each of the following as product of powers of their prime factors :
(v) $432$

Q.

Write the exponential form :-

$-p\times -p\times -p$

Q.

Identify the greater number in $4^3$ or $3^4$.

Q.

Write the greatest and the smallest $8$- digit numbers using the digits $3,2,1,0,8,7,6,5$ and find their difference.

Q.

If $15625=(x{)}^2=5^{\left(y\right)}$ . Find the value of $x$ and $y$. [3 MARKS]

Q.

Question 68

State whether the following statement is true or false:

If x and y are integers such that $x^2>y^2$, then $x^3>y^3$

Q.
Using the above pattern, find the value of the following: ​(i) $7^3-6^3$
(ii) ${12}^3-{11}^3$

Q.

Question 24

Write the correct answer from the given four options.

Given that, $\sqrt{4096}=64$, the value of $\sqrt{4096}+\sqrt{40.96}$ is

a) 74
b) 60.4
c) 64.4
d) 70.4

Q.

A piece of cloth of length 'x' is divided into three equal parts. Find the length of each part of the cloth.

1. 

2. 

3. 3x

4. 

Q.

Express the following as kilometre (km) using decimals.

$5km56m$

Q.

Solve the following problems:

The length of a rectangle is three times its breadth. If the perimeter is $88$cm, find the length and breadth.

Q.

Between $2^{10}$ and ${10}^2$ , ${10}^2$ is greater.

1. True

2. False

Q.

The distance between Earth and Mars is 2.2253x${10}^8$ kms. The distance between Mars and Saturn is $1.19666\times {10}^9$ kms. A spaceship starts from Earth and flies to Saturn via Mars. Find the total distance covered by the spaceship in metres.

1. 1.41919x${10}^{12}$ m

2. 14191900000

3. 1419190000000

4. 1.41919x${10}^9$ km

Q.

Identify the greater number in $5^3$ or $3^5$.

Q. Write the sum of powers of prime factors of 196.