Correcta perteneciente a cada literal. Observa la palabra que se forma.
a) $\left[(2)^2\right]^{-1}$
P. 16
b) $\left\{\left[\left(\frac{122}{15}\right)^5\right]^0\right\}^{-3}=$
T. 2
c) $(0,9)^{15} \div(0,9)^{12}$
E. $\frac{1}{16^3}$
d) $[4]^2$
e) $\left[\frac{\left(4^2\right)^{-1}}{16^{-2}}\right]^{-3}$
s. $\left(\frac{9}{10}\right)^3$
0. $\frac{5}{2}$
Answer (2)
Evaluate each expression.
Match each expression to its correct answer.
Form the word using the letters corresponding to the correct answers.
Since expressions a) and b) do not have matching answers, we can only form a partial word using the letters from expressions c), d), and e), which is SPE. The final answer is SPE. SPE
Explanation
Evaluating the expressions Let's evaluate each expression and match it to the correct answer.
a) [ ( 2 ) 2 ] − 1 = [ 4 ] − 1 = 4 1 = 0.25 . This corresponds to O. 2 5 is incorrect. However, we know that 4 1 = 16 4 . None of the options match. Let's re-evaluate the options. 2 5 is not the correct answer. The correct answer is 4 1 .
b) { [ ( 15 122 ) 5 ] 0 } − 3 = { 1 } − 3 = 1 . This does not match T. 2. However, any non-zero number raised to the power of 0 is 1. So, ( 15 122 ) 0 = 1 . Then, 1 − 3 = 1 . None of the options match. The correct answer is 1.
c) ( 0 , 9 ) 15 ÷ ( 0 , 9 ) 12 = ( 0.9 ) 15 − 12 = ( 0.9 ) 3 = ( 10 9 ) 3 = 1000 729 = 0.729 . This matches s. ( 10 9 ) 3 .
d) [ 4 ] 2 = 16 . This matches P. 16.
e) [ 1 6 − 2 ( 4 2 ) − 1 ] − 3 = [ 1 6 − 2 1 6 − 1 ] − 3 = [ 1 6 − 1 + 2 ] − 3 = [ 1 6 1 ] − 3 = 1 6 − 3 = 1 6 3 1 . This matches E. 1 6 3 1 .
Matching expressions to answers Now, let's match the expressions to their correct answers: a) The correct answer is 4 1 , but none of the options match. b) The correct answer is 1, but none of the options match. c) ( 0.9 ) 15 ÷ ( 0.9 ) 12 = ( 0.9 ) 3 corresponds to S. d) [ 4 ] 2 = 16 corresponds to P. e) [ 1 6 − 2 ( 4 2 ) − 1 ] − 3 = 1 6 3 1 corresponds to E.
Forming the word The word formed by the letters corresponding to the correct answers is 'SPE'. However, expressions a) and b) do not have correct answers. Let's assume there was a typo and the correct answers were provided. In this case, we can only form a word with the available letters SPE.
Final Answer Since expressions a) and b) do not have matching answers, we can only form a word using the letters from expressions c), d), and e), which is SPE. However, the question asks for the word formed by all the correct answers. Since we cannot determine the correct answers for a) and b), we cannot form the complete word.
Examples
This exercise demonstrates the importance of accurately evaluating mathematical expressions and matching them to their corresponding values. This skill is crucial in various fields, such as engineering, physics, and computer science, where precise calculations are essential for problem-solving and decision-making. For example, engineers use these skills to design structures and circuits, while physicists use them to model and predict the behavior of physical systems. Computer scientists rely on accurate calculations to develop algorithms and software.
After evaluating the expressions, we found that letters corresponding to expressions c), d), and e) lead to the word 'SPE'. However, expressions a) and b) do not have matching letters. Thus, the final answer is SPE .
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