For any two non-zero rational numbers x and y, x⁵ ÷ y⁵ is equal to.

1

(a)

(x ÷ y)¹

(b)

(x ÷ y)⁰

(c)

(x ÷ y)⁵

(d)

(x ÷ y)¹⁰

(- 4)⁴ x (-2)⁰  x (-1)²⁰² is equal to

1

(a)

64

(b)

1

(c)

0

(d)

256

(5⁷ ÷ 5²) x (3⁶ ÷ 3²)is equal to

1

(a)

1426

(b)

1242

(c)

253125

(d)

101962

Standard form corresponding to the number 654300100 is

1

(a)

6.543001 X10⁷

(b)

6.543001 x10⁸

(c)

6.543 x10⁸

(d)

6.543001 x 10⁹

Which of the following is the exponential form of '243' ?

1

(a)

3²

(b)

2³

(c)

3⁵

(d)

5³

If a^x = 1, then the value of x is _______ where a ≠ 1.

1

(a)

0

432 = 2⁴ x 3 .........

1

(a)

3³

< ,> or = sign. 2³ ...... 3²

1

(a)

2³ < 3²

10000 _____ 10⁵

1

(a)

10000 < 10⁵

1 million = 10^____

1

(a)

6

2⁰ x 3⁰ x 0¹ x 2¹³⁶ = 1

1

(a) True

(b) False

876543 = 8 x 10⁵ + 7 x 10⁴ + 6 x 10³ + 5 x 10² + 4 x 10¹ +3 x10⁰

1

(a) False

(b) True

(2⁵)⁶ = 2¹¹

1

(a) True

(b) False

9001006001 =9 x 10⁹ + 1 x 10⁶ + 6 x 10³ +1 x 10⁰

1

(a) False

(b) True

(-3)⁴= -12

1

(a) True

(b) False

Solve: \((\frac{6}{7})^5+(\frac{6}{7})^3\)

2

(a)

\((\frac{6}{7})^{5-3}=(\frac{6}{7})^2=\frac{36}{49}\)

What is the base of (b)²⁵?

2

(a)

b

Find 2° + 3° + 4°.

2

(a)

3

Simplify 3 x 4⁴

2

(a)

Write base and exponent of the following numbers: 7³

2

(a)

Express the following numbers in the exponential form: 3 x 3 x 5 x 5 x 7 x 7

2

(a)

Simplify the following: 7³ x 2³

2

(a)

Using laws of exponents, a^m\(\div\)  a ⁿ = a^m-n, simplify and write the answer in exponential form: (-3)⁷ \(\div\)(-3)⁵

2

(a)

Write the standard form of the following numbers: 123870000000

2

(a)

Find the value of 2⁵ x 4² x 2²

2

(a)

1. Find the value of 2⁶

   2

   (a)

2. Express each of the following numbers using  exponential notation: 343

   2

   (a)

1. \(\frac { { 12 }^{ 4 }\times { 9 }^{ 3 }\times 4 }{ { 6 }^{ 3 }\times { 8 }^{ 2 }\times 27 } \)

   2

   (a)

2. Evaluate: 2¹⁴\(\div\)2¹²

   2

   (a)

1. Simplify \(\frac { { 5 }^{ -2 }\times { 3 }^{ -3 }\times (125)^{ 2/3 } }{ (27)^{ -2/3 }\times (32)^{ -1/5 } } \).

   5

   (a)

2. Find the value of x, such that \({ \left( \frac { 1 }{ 5 } \right) }^{ 5 }\times { \left( \frac { 1 }{ 5 } \right) }^{ 19 }={ \left( \frac { 1 }{ 5 } \right) }^{ 8x }\) .

   5

   (a)

1. Simplify:
   (i) \({ \left[ { \left\{ { \left( -\frac { 1 }{ 4 } \right) }^{ 2 } \right\} }^{ -2 } \right] }^{ -1 }\)
   (ii) \({ \left( -\frac { 3 }{ 2 } \right) }^{ 3 }\div { \left( -\frac { 3 }{ 2 } \right) }^{ 6 }\)

   5

   (a)

2. Express the following in exponential form:
   [(2³)² x 3⁶]. X 5⁶

   5

   (a)

If \(\frac { p }{ q } ={ \left( \frac { -2 }{ 3 } \right) }^{ 9 }\div { \left( \frac { -2 }{ 3 } \right) }^{ 8 }\) then find the value of \({ \left( \frac { p }{ q } \right) }^{ 2 }\)

4

(a)

If 2¹⁹⁹⁸- 2¹⁹⁹⁷- 2¹⁹⁹⁶+ 2¹⁹⁹⁵= k.2¹⁹⁹⁵, then the value of k is?

4

(a)