f) [tex]\frac{\left(\frac{2}{5}\right)^{-2}}{\left(\frac{5}{2}\right)\left(\frac{5}{2}\right)} \times 2[/tex]
R. [tex]\frac{1}{4}[/tex]
g) [tex]\frac{25^{-1}}{5^{-2}} \div \frac{0,05^{-2}}{0,1^{-3}} \mu c+[/tex]
E. 1
Answer (2)
Simplify expression f): ( 2 5 ) ( 2 5 ) ( 5 2 ) − 2 × 2 = 2 .
The given answer for f) is incorrect.
Simplify expression g): 5 − 2 2 5 − 1 ÷ 0 , 1 − 3 0 , 0 5 − 2 = 2 5 = 2.5 .
The given answer for g) is incorrect. The correct answers are f ) = 2 , g ) = 2.5
Explanation
Problem Analysis We are given two expressions to simplify and verify their respective answers.
Expression f) is: ( 2 5 ) ( 2 5 ) ( 5 2 ) − 2 × 2
Expression g) is: 5 − 2 2 5 − 1 ÷ 0 , 1 − 3 0 , 0 5 − 2
Simplifying Expression f) Let's simplify expression f) step by step. Recall that ( b a ) − n = ( a b ) n . Therefore, ( 5 2 ) − 2 = ( 2 5 ) 2 = 4 25 .
The denominator is ( 2 5 ) ( 2 5 ) = 4 25 .
So the expression becomes: 4 25 4 25 × 2 = 1 × 2 = 2
Comparison for f) The simplified expression f) is 2, but the expected answer is 4 1 . Therefore, the given answer is incorrect.
Simplifying Expression g) Now let's simplify expression g) step by step. Recall that a − n = a n 1 . Therefore, 2 5 − 1 = 25 1 and 5 − 2 = 25 1 .
The numerator becomes 25 1 25 1 = 1 .
We have 0.05 = 100 5 = 20 1 and 0.1 = 10 1 .
Then, 0.0 5 − 2 = ( 20 1 ) − 2 = 2 0 2 = 400 and 0. 1 − 3 = ( 10 1 ) − 3 = 1 0 3 = 1000 .
The denominator becomes 1000 400 = 10 4 = 5 2 .
So the expression becomes: 1 ÷ 5 2 = 1 × 2 5 = 2 5 = 2.5
Comparison for g) The simplified expression g) is 2 5 or 2.5, but the expected answer is 1. Therefore, the given answer is incorrect.
Final Answer In summary, the correct answer for expression f) is 2, and the correct answer for expression g) is 2.5. The provided answers are both incorrect.
Examples
Understanding how to simplify exponential expressions is crucial in many fields, such as physics and engineering, where exponential growth and decay are common. For example, calculating the decay rate of a radioactive substance or the growth of a bacterial population involves simplifying expressions with exponents. These calculations help scientists and engineers make accurate predictions and design effective solutions.
The correct simplification for expression f) is 2, while for g) it is 2.5, both of which differ from the provided answers. Therefore, the answers for both expressions are incorrect.
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