Express each number in the exponential form: 1 243

The given number is 1 243 . ∴ 1 243 = 1 × 1 × 1 × 1 × 1 3 × 3 × 3 × 3 × 3 ⇒ 1 243 = 1 3 5 Hence, 1 3 5 is the exponential form of the given number.

Express each number in the exponential form: - 1000 343

Given: - 1000 343 The exponential form is an easier way of writing repeated multiplication involving base and exponents. Hence, - 1000 343 = - 10 × - 10 × - 10 7 × 7 × 7 = - 10 7 3

Express each number in the exponential form: 25 36

The given number is 25 36 . ∴ 25 36 = 5 × 5 2 × 2 × 3 × 3 = 5 × 5 6 × 6 ⇒ 25 36 = 5 6 2 Hence, 5 6 5 is the exponential form of the given number.

Identify the greater number in pair of numbers. 2 3 2 or - 3 2 2

We know, We use exponents as a shortcut to represent repeated multiplication. When a number is multiplied with itself 2 or more times, then we represent it in exponent form. It can be generalised as a × a × a × . . . × n times = a n , where a is any non-zero number and n is a natural number and it is read as " a to the power n or a raised to the power n ". Here ' a ' is called the base and ' n ' is called the exponent or index. a 2 is also called as a squared and a 3 is also called as a cubed. If power of - 1 is odd, then the value is - 1 and if the power is even, then the value is 1 . That is, - 1 odd number = - 1 and - 1 even number = 1 Given, 2 3 2 or - 3 2 2 The value of 2 3 3 = 2 3 × 2 3 × 2 3 = 2 3 3 3 = 8 27 = 0 . 296 The value of - 3 2 2 = - 3 2 × - 3 2 = 9 4 = 2 . 25 0 . 296 > 2 . 25 Hence, the greater number is - 3 2 2 .

Identify the greater number in pair of numbers. - 4 5 2 or 4 5 3

We know, We use exponents as a shortcut to represent repeated multiplication. When a number is multiplied with itself 2 or more times, then we represent it in exponent form. It can be generalised as a × a × a × . . . × n times = a n , where a is any non-zero number and n is a natural number and it is read as " a to the power n or a raised to the power n ". Here ' a ' is called the base and ' n ' is called the exponent or index. a 2 is also called as a squared and a 3 is also called as a cubed. If power of - 1 is odd, then the value is - 1 and if the power is even, then the value is 1 . That is, - 1 odd number = - 1 and - 1 even number = 1 Given, The value of - 4 5 2 = - 4 5 × - 4 5 = 16 25 = 0 . 64 The value of 4 5 3 = 4 5 × 4 5 × 4 5 = 64 125 = 0 . 512 0 . 64 > 0 . 512 Hence, the greater number is - 4 5 2 .