Perform the indicated operation: $\left(\frac{1}{2}\right)^2-\sqrt{16}+\left(\frac{7}{4}\right)\left(\frac{16}{28}\right)$
Answer (2)
First, we evaluate each part of the expression, which results in − 4 11 after combining the results. The breakdown involves calculating the square, the square root, and the multiplication of fractions. The final answer is − 4 11 .
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Evaluate each term separately:
( 2 1 ) 2 = 4 1
16 = 4
( 4 7 ) ( 28 16 ) = 1
Substitute the values back into the expression: 4 1 − 4 + 1
Combine the terms: 4 1 − 4 + 1 = − 4 11
The final answer is − 4 11
Explanation
Understanding the Expression We are asked to evaluate the expression ( 2 1 ) 2 − 16 + ( 4 7 ) ( 28 16 ) . This involves basic arithmetic operations.
Evaluating Each Term First, let's evaluate each term separately.
( 2 1 ) 2 = 2 1 × 2 1 = 4 1
16 = 4
( 4 7 ) ( 28 16 ) = 4 7 × 28 16 = 4 × 28 7 × 16 = 112 112 = 1
Substituting the Values Now, substitute the evaluated terms back into the expression: 4 1 − 4 + 1
Combining the Terms Combine the terms: 4 1 − 4 + 1 = 4 1 − 3 = 4 1 − 4 12 = − 4 11
Final Result The final result is − 4 11 .
Examples
Understanding how to evaluate expressions with fractions, exponents, and square roots is fundamental in many areas, such as physics and engineering. For example, when calculating the kinetic energy of an object, you need to square the velocity (exponentiation) and might need to find the square root of a value to determine speed. Similarly, these skills are crucial in financial calculations, such as determining investment returns or calculating areas and volumes in construction projects. Mastering these basic operations provides a strong foundation for more complex problem-solving.
