Find the unknown value in the following number. 5.48454 × 10 b = 548454

We need to find the value of b in 5 . 48454 × 10 b = 548454 . LHS = 5 . 48454 × 10 b ..... i RHS = 548454 Now, we will convert 548454 in standard exponential form. We know that, A number is in standard form when it is written as a × 10 n , where a is a decimal number greater than or equal to 1 and less than 10 and n is a positive integer. Thus, 548454 = 5 . 48454 × 100000 = 5 . 48454 × 10 5 Thus, RHS = 548454 = 5 . 48454 × 10 5 ... ii By comparing i and ii , we have 5 . 48454 × 10 b = 5 . 48454 × 10 5 ⇒ 10 b = 10 5 ∵ if a n = a m then m = n ⇒ b = 5 Hence, the unknown value is 5 .

Write the following in exponential form. 5 × 5 × 2 × a × a × a

Given expression as, 5 × 5 × 2 × a × a × a Here we can see 5 is multiplied by itself 2 times, 2 is multiplied by itself 1 times and a is multiplied by itself 3 times. So, we can write given expression as, 5 × 5 × 2 × a × a × a = 5 2 × 2 1 × a 3 Where 5 , 2 and a are base and 2 , 1 and 3 are their exponents. Hence, the exponential form of 5 × 5 × 2 × a × a × a = 5 2 × 2 1 × a 3 .

Find the unknown value in the following number. 7.65758 × 10 f = 765758

We need to find the value of f in 7 .65758 × 10 f = 765758 . LHS = 7 .65758 × 10 f ..... i RHS = 765758 Now, we will convert 765758 in standard exponential form. We know that, A number is in standard form when it is written as a × 10 n , where a is a decimal number greater than or equal to 1 and less than 10 and n is a positive integer. Thus, 765758 = 7 . 65758 × 100000 = 7 . 65758 × 10 5 Thus, RHS = 765758 = 7 . 65758 × 10 5 ... ii By comparing i and ii , we have = 7 . 65758 × 10 f = 7 . 65758 × 10 5 ⇒ 10 f = 10 5 ⇒ f = 5 ∵ If a n = a m then m = n Hence, the unknown value is 5 .

Find the unknown value in the following number. 2.8748 × 10 a = 28748

We need to find the value of a in 2.8748 × 10 a = 28748 . LHS = 2 . 8748 × 10 a ..... i RHS = 28748 Now, we will convert 28748 in standard exponential form. We know that, A number is in standard form when it is written as a × 10 n , where a is a decimal number greater than or equal to 1 and less than 10 and n is a positive integer. Thus, 28748 = 2 . 8748 × 10000 = 2 . 8748 × 10 4 Thus, RHS = 28748 = 2 . 8748 × 10 4 ... ii By comparing i and ii , we have 2 . 8748 × 10 a = 2 . 8748 × 10 4 ⇒ 10 a = 10 4 ⇒ a = 4 ∵ if a n = a m then m = n Hence, the unknown value is 4 .

Write the following in exponential form. m × m × m × m × m

Given expression is, m × m × m × m × m Here we can see m is multiplied five times by itself. So, we can write it as m × m × m × m × m = m 5 It is read as m to the power 5 . Here, m is the base and 5 is the exponent. Hence, the exponential form of m × m × m × m × m is m 5 .

Find the unknown value in the following number. 7 . 0241 × 10 d = 70241

We need to find the value of d in 7 . 0241 × 10 d = 70241 . LHS = 7 . 0241 × 10 d ..... i RHS = 70241 Now, we will convert 70241 in standard exponential form. We know that, A number is in standard form when it is written as a × 10 n , where a is a decimal number greater than or equal to 1 and less than 10 and n is a positive integer. Thus, 70241 = 7 . 0241 × 10000 = 7 . 0241 × 10 4 Thus, RHS = 70241 = 7 . 0241 × 10 4 ... ii By comparing i and ii , we have = 7 . 0241 × 10 d = 7 . 0241 × 10 4 ⇒ 10 d = 10 4 ⇒ d = 4 ∵ if a n = a m then m = n Hence, the unknown value is 4 .

Find the unknown value in the following number. 6 . 5865 × 10 e = 65865

We need to find the value of e in 6 . 5865 × 10 e = 65865 . LHS = 6 . 5865 × 10 e ..... i RHS = 65865 Now, we will convert 65865 in standard exponential form. We know that, A number is in standard form when it is written as a × 10 n , where a is a decimal number greater than or equal to 1 and less than 10 and n is a positive integer. Thus, 65865 = 6 . 5865 × 10000 = 6 . 5865 × 10 4 Thus, RHS = 65865 = 6 . 5865 × 10 4 ... ii By comparing i and ii , we have 6 . 5865 × 10 e = 6 . 5865 × 10 4 ⇒ 10 e = 10 4 ⇒ e = 4 ∵ If 4 6 = 4 x then x = 6 Hence, the unknown value is 4 .