Introduction

Q.

$198,194,185,169,\_\_?,$ What will be the next number$?$

Q. 1 raised to any power is always 1.

1. False
2. True

Q.

How many ways can a $7$ letter word be arranged.

Q. What is the value of '2 raised to power of 3'?

1. 4
2. 8
3. 12
4. 16

Q.

The division comparison of two quantities of the same type is called a ______.

Q.

What is the sum of 3 raised to power 2 and 4 raised to power 2?

1. 7

2. 25

3. 18

4. 5

Q.

Using laws of exponents, simplify and write the answer in exponential form:

(i) 3² × 3⁴ × 3⁸ (ii) 6¹⁵ ÷ 6¹⁰ (iii) a³ × a²

(iv) 7^x× 7² (v) (vi) 2⁵ × 5⁵

(vii) a⁴ × b⁴ (viii) (3⁴)³

(ix) (x) 8^t ÷ 8²

Q. Square is a regular polygon.

1. False
2. True

Q.

Express the exponential form with prime number as base.

(1) 4

(2) 8

(3) 16

(4) 49

(5) 81

Q. Find the value of $\frac{100}{10000}$.

1. ${10}^3$
2. ${10}^{-3}$
3. ${10}^{-2}$
4. ${10}^2$

Q.

What is the sum of 3 raised to power 2 and 4 raised to power 2?

1. 18

2. 7

3. 5

4. 25

Q. 10 raised to power 6 = ______.

1. 100000
2. 1000000
3. 1000
4. 10000

Q.

Express each of the following as a product of prime factors only in exponential form:

(i) 108 × 192 (ii) 270

(iii) 729 × 64 (iv) 768

Q.

Represent 1024 in exponent form with base 2.

1. 2⁸

2. 2⁹

3. 2¹⁰

4. 2¹¹

Q. 1 raised to any power is always 1.

1. True
2. False

Q. If A : B = 5 : 6 and B : C = 4 : 7, find A : B : C.

Q. Evaluate :
i) $(0.9{)}^2$

Q.

If $m=2$ and $n=-2$, find the value of $6m^3+4n^{-2}$

1. $40$

2. $49$

3. $37$

4. $42$

Q.

Say true or false and justify your answer:

(i) 10 × 10¹¹ = 100¹¹ (ii) 2³ > 5²

(iii) 2³ × 3² = 6⁵ (iv) 3⁰ = (1000)⁰

Q. What is 2 raised to power 5?

1. 10
2. 32
3. 16
4. 64

Q.

Expand the following exponential numbers:

(1) 2³

(2) 3²

(3) (−4)⁴

(4)

(5) (5²)³

Q. How many cubes are required to visualise $3^4$?

1. 20
2. 81
3. 12
4. 18

Q. 36 can be expressed as ____.

1. 2 X 2 X 2 X 3
2. 2 X 2 X 2 X 2
3. 2 X 2 X 3 X 3
4. 2 X 3 X 3

Q. The value of $5^{-5}=$ ____.

1. $\frac{1}{5}\times \frac{1}{5}\times \frac{1}{5}\times \frac{1}{5}$
2. $\frac{1}{5^5}$
3. $\frac{1}{5}\times \frac{1}{5}\times \frac{1}{5}\times \frac{1}{5}\times \frac{1}{5}$
4. $\frac{1}{5^{-5}}$

Q.

Express the following as powers of rational numbers;

729/216 and 144/625

Q. Expanded form of 282.42=$2\times {10}^2+8\times {10}^1+2\times {10}^0+$$+2\times {10}^{-2}$.

1. $4\times {10}^{-1}$
2. $4\times {10}^{-2}$
3. $4\times {10}^1$
4. $4\times {10}^2$

Q. In the cube given below, if one unit cube represents $2^0$, then express what will the whole cube represent, as a power of 2?

1. $2^3$
2. $2^4$
3. $2^2$
4. $2^1$

Q. If the values of x, y, z and p are 1, 2, 3 and 4 respectively, then find the value of $x^y+z^p$.

1. 80
2. 83
3. 81
4. 82

Q. If 3 is multiplied by itself ten times, it can be written as ____

1. $3^{10}$
2. $3\times 10$
3. 3+10
4. ${10}^3$

Q.

We cut a corner of a cube as shown in the figure. The cut out piece is _________.