#### 3^{2} 3^{3}= ____.

3^{2} 3^{3} = 3^{2+3} ( a^{m} a^{n} = a^{m+n}) = 3^{5} = 243 ∴ 3^{2} 3^{3}= 243

#### Non-terminating and non-recurring decimals are called rational numbers.

Non-terminating and non-recurring decimals are called irrational numbers.

#### The number of rational numbers between two natural numbers is infinite.

The number of rational numbers between two natural numbers is infinite.

#### The decimal expansion of 144 /400 is ____

144 /400=36 /100 =0.36 Hence, the decimal expansion of 144 /400 is terminating.

#### A non-terminating and non-recurring decimal is known as an irrational number.

A non-terminating and non-recurring decimal is known as an irrational number.

#### IF m^{n} = 125, then (m -1)^{n+1}= ____.

Given
m^{n} = 125 ⇒ m^{n } = 5^{3 } ⇒ m = 5 and n =3 (m -1)^{n+1 }= (5 – 1)^{3+1 } = 4^{4} =256 (m -1)^{n+1} = 256

#### The solutions of the equation x^{2}−9=0 are irrational numbers.

Given equation is x^{2}−9=0.
⇒ x^{2} = 9
⇒x=9
⇒x=±3
3 and −3 are rational numbers.
Hence, the solutions of x^{2}−9=0 are rational numbers.

#### Which of the following is a rational number?

0.3333333... is a non-terminating and recurring decimal. We know that, a non-terminating and recurring decimal can be converted to the form of pq, where p, q are integers and q ≠ 0. 0.3333333... = 13 Hence, 0.3333333... Is a rational number.

#### Every whole number is a natural number.

'0' is a whole number but not a natural number. Hence, every whole number except 0 is a natural number.