Chapter 11: Exponents and Powers

Solution:-

False.

We know that, 1 million = 10,00,000

= 10⁶

Solution:-

True.

We know that, 1 hour = 60 minutes

1 minutes = 60 seconds

Therefore, 1 hour = 60 × 60 = 3600 seconds

Solution:-

False

1⁰ = 1

0¹ = 0

So, 1 × 0 = 0

Solution:-

False.

(-3)⁴ = -3 × -3 × -3 × -3 = 81

So, 81 ≠ – 12

Solution:-

True.

3⁴ = 3 × 3 × 3 × 3 = 81

4³ = 4 × 4 × 4 = 64

Therefore, 81 > 64

Solution:-

True.

Consider the LHS = (-3/5)¹⁰⁰

-3 can be written as = (-1 × 3)

So, ((-1 × 3)/5)¹⁰⁰

= (-1¹⁰⁰ × 3¹⁰⁰)/5¹⁰⁰

= (1 × 3¹⁰⁰)/5¹⁰⁰

= 3¹⁰⁰/5¹⁰⁰

Then, consider the RHS = -3¹⁰⁰/-5¹⁰⁰

= 3¹⁰⁰/5¹⁰⁰

By comparing LHS and RHS,

LHS = RHS

3¹⁰⁰/5¹⁰⁰ = 3¹⁰⁰/5¹⁰⁰

Therefore, (-3/5)¹⁰⁰ = (-3¹⁰⁰/-5¹⁰⁰)

Solution:-

False.

For any non-zero integers ‘a’ and ‘b’ and whole numbers m and n,

a^m × aⁿ = a^m+n

Solution:-

True.

we know that, x⁰ = 1

so, x⁰ × x⁰ = 1 × 1 = 1

x⁰ ÷ x⁰ = 1 ÷ 1 = 1

Therefore, x⁰ × x⁰ = x⁰ ÷ x⁰

1 = 1

Solution:-

False

Any number can be expressed as a decimal number between 1.0 and 10.0 (including 1.0) multiplied by a power of 10. Such form of a number is called its standard form or scientific notation.

Solution:-

False.

4² = 4 × 4 = 16

2⁴ = 2 × 2 × 2 × 2 = 16

Therefore, 4² = 2⁴