81 × 81 to be expressed as power of 3 .

Given, 81 × 81 We know, 81 = 3 × 3 × 3 × 3 81 × 81 = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 If a m = a × a × a × a × . . . . . . . . . m times, is the expanded form of the exponent a m , Where a is the base and m is the exponent. In the given expression, 3 is multiplied 8 times. ∴ 81 × 81 = 3 8 Hence, the exponential form of the given expression is 3 8 .

81 × 81 to be expressed as power of 3 .

Given, 81 × 81 We know, 81 = 3 × 3 × 3 × 3 81 × 81 = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 If a m = a × a × a × a × . . . . . . . . . m times, is the expanded form of the exponent a m , Where a is the base and m is the exponent. In the given expression, 3 is multiplied 8 times. ∴ 81 × 81 = 3 8 Hence, the exponential form of the given expression is 3 8 .

Find the value of the given exponents: 5 9 × 5 6 5 7

We have to find the value of 5 9 × 5 6 5 7 . If a and b are two integers and m is also an integer then a × b m = a m × b m . ⇒ 5 9 × 5 6 5 7 = 5 9 + 6 5 7 = 5 15 5 7 If a is a non-zero integer and m and n are also integers, then a m ÷ a n = a m a n = a m - n ⇒ 5 15 5 7 = 5 15 - 7 = 5 8 Hence, the required answer is 5 8 .

Find the value of the given exponents a 7 a 5 × a 2 where a ≠ 0

We have to find the value of a 7 a 5 × a 2 . If x is a non-zero integer and m and n are also integers, then x m ÷ x n = x m x n = x m - n . ⇒ a 7 a 5 × a 2 = a 7 - 5 × a 2 = a 2 × a 2 If x is a non-zero integer and m and n are also integers, then x m × x n = x m + n . ⇒ a 2 × a 2 = a 2 + 2 = a 4 Hence, the required answer is a 4 .

Find the value of the given exponents: 3 × 7 2 × 2 4 21 × 112

We have to find the value of 3 × 7 2 × 2 4 21 × 112 . We have to express 21 and 112 in form of exponents by factorisation. 2 112 2 56 2 28 2 14 7 7 1 ⇒ 112 = 2 4 × 7 , 21 = 3 × 7 ⇒ 3 × 7 2 × 2 4 21 × 112 = 3 × 7 2 × 2 4 3 × 7 × 2 4 × 7 = 3 × 7 2 × 2 4 3 × 7 2 × 2 4 If a is a non-zero integer and m and n are also integers, then a m ÷ a n = a m a n = a m - n . ⇒ 3 × 7 2 × 2 4 3 × 7 2 × 2 4 = 3 1 - 1 × 7 2 - 2 × 2 4 - 4 = 3 0 × 7 0 × 2 0 If a is an integer then, a 0 = 1 . ⇒ 3 0 × 7 0 × 2 0 = 1 × 1 × 1 = 1 Hence, the required answer is 1 .