Evaluate the expression: $-5+28^0+6^2$.
A) 59
B) 32
C) 35
D) 8
Answer (2)
Evaluate 2 8 0 = 1 .
Evaluate 6 2 = 36 .
Substitute the values into the expression: − 5 + 1 + 36 .
Perform the arithmetic: − 5 + 1 + 36 = 32 . The answer is 32 .
Explanation
Understanding the Problem We are asked to evaluate the expression − 5 + 2 8 0 + 6 2 and choose the correct answer from the given options.
Evaluating the Exponent First, let's evaluate 2 8 0 . Any non-zero number raised to the power of 0 is equal to 1. Therefore, 2 8 0 = 1 .
Evaluating the Square Next, let's evaluate 6 2 . This means 6 multiplied by itself, so 6 2 = 6 × 6 = 36 .
Substituting the Values Now, substitute the calculated values back into the original expression: − 5 + 2 8 0 + 6 2 = − 5 + 1 + 36
Performing the Arithmetic Perform the addition and subtraction from left to right: − 5 + 1 + 36 = − 4 + 36 = 32
Finding the Correct Answer The final value of the expression is 32. Comparing this to the given options, we see that option B is the correct answer.
Examples
Understanding how to evaluate expressions with exponents and arithmetic operations is fundamental in many areas, such as calculating compound interest, determining the growth of populations, or analyzing the decay of radioactive substances. For example, if you invest $100 at an annual interest rate of 5% compounded annually, the amount you have after 3 years can be calculated using the expression 100 ( 1 + 0.05 ) 3 . Evaluating such expressions accurately is crucial for making informed financial decisions.
The value of the expression − 5 + 2 8 0 + 6 2 is evaluated to be 32. Thus, the correct answer is B) 32. This process involved evaluating the exponent and the square before performing the arithmetic operations.
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