For a > 0 and rational m, n, which of these statements is FALSE?

Class 9Number SystemsNumber Systems

Step-by-Step Solution

Exponents are added only when powers are MULTIPLIED. Adding two powers has no such shortcut: for example

2^{2} + 2^{3} = 4 + 8 = 12

, while

2^{5} = 32

. The first three statements are the genuine laws of exponents.

Answer: D)

a^{m} + a^{n} = a^{m + n}

**Sum/difference of two irrationals can be rational.** Example:

(1 + 2) + (1 - 2) = 2

.
**Product of two irrationals can be rational.** Example:

2 \times 2 = 2

.
**Sum of a rational and an irrational is always irrational.**

3 + 2

is irrational.
**Product of a non-zero rational and an irrational is always irrational.**

5 \times 2

is irrational.

These facts let you build new irrationals and prove things irrational by contradiction.

Don't just memorise the answer — build a daily practice habit.