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}}+\frac{0,05^{-2}}{0,1^{-3}} \uparrow[/tex]
E. 1
Answer (2)
Simplify expression f) using exponent rules and fraction division, resulting in 2.
Simplify expression g) using exponent rules and decimal operations, resulting in 1.4.
Compare the calculated results with the provided answers.
The provided answers for both expressions are incorrect: f) should be 2, and g) should be 1.4.
Explanation
Problem Analysis We are given two expressions to simplify and verify if the provided answers are correct.
Expression f) is: ( 2 5 ) ( 2 5 ) ( 5 2 ) − 2 × 2 The provided answer is 4 1 .
Expression g) is: 5 − 2 2 5 − 1 + 0 , 1 − 3 0 , 0 5 − 2 The provided answer is 1.
Simplifying Expression f) Let's simplify expression f) step by step. First, we need to evaluate ( 5 2 ) − 2 . Recall that a − n = a n 1 . Therefore, ( 5 2 ) − 2 = ( 2 5 ) 2 = 2 2 5 2 = 4 25 Next, we have ( 2 5 ) ( 2 5 ) = 4 25 .
So, expression f) becomes: 4 25 4 25 × 2 = 1 × 2 = 2 Thus, the simplified expression f) is 2, while the provided answer is 4 1 .
Simplifying Expression g) Now, let's simplify expression g). We have: 5 − 2 2 5 − 1 + 0 , 1 − 3 0 , 0 5 − 2 First, let's rewrite the expression using fractions: 25 1 25 1 + 0. 1 3 1 0.0 5 2 1 This simplifies to: 1 + 0.0 5 2 0. 1 3 = 1 + 0.0025 0.001 = 1 + 2.5 1 = 1 + 2 5 1 = 1 + 5 2 = 1 + 0.4 = 1.4 Thus, the simplified expression g) is 1.4, while the provided answer is 1.
Final Answer In conclusion, the simplified expression f) is 2, which does not match the provided answer of 4 1 . The simplified expression g) is 1.4, which does not match the provided answer of 1.
Final Conclusion The correct answer for f) is 2 and the correct answer for g) is 1.4.
Examples
Understanding how to simplify exponential and fractional expressions is crucial in many fields, such as physics and engineering. For example, when calculating the decay rate of a radioactive substance or determining the impedance in an electrical circuit, you need to manipulate exponential terms and fractions. Mastering these skills allows for accurate modeling and prediction of real-world phenomena.
The simplified result for expression f) is 2, and for expression g) it is 1.4. Neither result matches the provided answers of 4 1 and 1, respectively.
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