Write the following number in exponential form. 14641 625

We know that, a m means a multiplied to itself m times. Here a is called the base and m is called an exponent. We need to find the exponential form of 14641 625 To write a given number in exponential form, we need to find the prime factorisation of the number. Using prime factorisation, we get 14641 = 11 × 11 × 11 × 11 = 11 4 625 = 5 × 5 × 5 × 5 = 5 4 Hence, the exponential form of 14641 625 is 11 5 4

Write the following number in exponential form. 256 6561

We know that, a m means a multiplied to itself m times. Here a is called the base and m is called an exponent. We need to find the exponential form of 256 6561 To write a given number in exponential form, we need to find the prime factorisation of the number. Using prime factorisation, we get 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2 8 6561 = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 = 3 8 Hence, the exponential form of 256 6561 is 2 3 8

Evaluate the following. ( 2 3 ) 4

Given, ( 2 3 ) 4 We know that, a m means " a to the power of m " or " a multiplied by itself m times". Here, a is called the base and m is called the exponent. For any two non-zero integers a and b , a m ÷ b m = a m b m = a b m , where m is a whole number. ( 2 3 ) 4 = 2 4 3 4 ( 2 3 ) 4 = 2 × 2 × 2 × 2 3 × 3 × 3 × 3 ( 2 3 ) 4 = 16 81 Hence, the required answer is 16 81 .

Evaluate the following. ( - 1 9 ) 2

Given, ( - 1 9 ) 2 We know that, a m means " a to the power of m " or " a multiplied by itself m times". Here, a is called the base and m is called the exponent. For any two non-zero integers a and b , a m ÷ b m = a m b m = a b m , where m is a whole number. ( - 1 9 ) 2 = - 1 2 9 2 ( - 1 9 ) 2 = - 1 × - 1 9 × 9 ( - 1 9 ) 2 = 1 81 Hence, the required answer is 1 81 .

Evaluate the following. ( - 3 4 ) - 3

Given, ( - 3 4 ) - 3 We know that, a m means " a to the power of m " or " a multiplied by itself m times". Here, a is called the base and m is called the exponent. For any two non-zero integers a and b , a - m = 1 a m , where m is a whole number. ( - 3 4 ) - 3 = ( 4 - 3 ) 3 ( - 3 4 ) - 3 = 4 × 4 × 4 - 3 × - 3 × - 3 ( - 3 4 ) - 3 = 64 - 27 = - 64 27 Hence, the required answer is - 64 27 .

Evaluate the following. ( - 2 5 ) 3

Given, ( - 2 5 ) 3 We know that, a m means " a to the power of m " or " a multiplied by itself m times". Here, a is called the base and m is called the exponent. For any two non-zero integers a and b , a m ÷ b m = a m b m = a b m , where m is a whole number. ( - 2 5 ) 3 = - 2 3 5 3 ( - 2 5 ) 3 = - 2 × - 2 × - 2 5 × 5 × 5 ( - 2 5 ) 3 = - 8 125 Hence, the required answer is - 8 125 .