Matching the Simplified Expressions:
Expression Matching Option
(4.5×10^4).(6.8×10^-8) 1.82×10^-4
(2.8×10^2).(6.5×10^-7) 3.06×10^-3
(5.6 × 10^-3). (7.7 × 10^-9)/ (8 x 10^-2). (3.5 × 10^-6) 1.54×10^-4
(7.4 × 10^-5). (3.8 × 10^3)/ (9.3 × 10^-4). (3.2 × 10^5) 9.45×10^-4
Expression 1:
(4.5 x 10^4) x (6.8 x 10^-8) = (4.5 x 6.8) x (10^4 x 10^-8)
Multiplication of exponents with the same base: 4.5 x 6.8 = 30.6 and 10^4 x 10^-8 = 10^(4-8) = 10^-4
Simplified expression: 30.6 x 10^-4 = 3.06 x 10^-3
Expression 2:
(2.8 x 10^2) x (6.5 x 10^-7) = (2.8 x 6.5) x (10^2 x 10^-7)
Multiplication of exponents: 2.8 x 6.5 = 18.2 and 10^2 x 10^-7 = 10^(2-7) = 10^-5
Simplified expression: 18.2 x 10^-5 = 1.82 x 10^-4
Expression 3:
[(5.6 x 10^-3) x (7.7 x 10^-9)] / [(8 x 10^-2) x (3.5 x 10^-6)]
Multiplication and division of exponents:
Numerator: (5.6 x 7.7) x (10^-3 x 10^-9) = 43.12 x 10^-12
Denominator: (8 x 3.5) x (10^-2 x 10^-6) = 28 x 10^-8
Simplified expression: (43.12 x 10^-12) / (28 x 10^-8) = 1.54 x 10^-4
Expression 4:
[(7.4 x 10^-5) x (3.8 x 10^3)] / [(9.3 x 10^-4) x (3.2 x 10^5)]
Multiplication and division of exponents:
Numerator: (7.4 x 3.8) x (10^-5 x 10^3) = 28.22 x 10^-2
Denominator: (9.3 x 3.2) x (10^-4 x 10^5) = 29.76 x 10^1
Simplified expression: (28.22 x 10^-2) / (29.76 x 10^1) = 9.