Which of these is equal to [tex]$5^0+2^1$[/tex]?
A. [tex]$2^0+2^1$[/tex]
B. [tex]$6^0-3^0$[/tex]
C. [tex]$2^0+1^1$[/tex]
D. [tex]$6^0-6^1$[/tex]
Answer (2)
Evaluate the expression: 5 0 + 2 1 = 1 + 2 = 3 .
Evaluate the first option: 2 0 + 2 1 = 1 + 2 = 3 .
Evaluate the second option: 6 0 − 3 0 = 1 − 1 = 0 .
Evaluate the third option: 2 0 + 1 1 = 1 + 1 = 2 .
Evaluate the fourth option: 6 0 − 6 1 = 1 − 6 = − 5 .
The first option is equal to the given expression: 2 0 + 2 1 .
Explanation
Understanding the problem We are given the expression 5 0 + 2 1 and we need to find an equivalent expression from the given options.
Evaluating the expression First, let's evaluate the given expression:
5 0 + 2 1 = 1 + 2 = 3
Remember that any number raised to the power of 0 is 1, and any number raised to the power of 1 is the number itself.
Evaluating the options Now, let's evaluate each of the given options:
Option 1: 2 0 + 2 1 = 1 + 2 = 3 Option 2: 6 0 − 3 0 = 1 − 1 = 0 Option 3: 2 0 + 1 1 = 1 + 1 = 2 Option 4: 6 0 − 6 1 = 1 − 6 = − 5
Finding the matching expression Comparing the value of the original expression ( 3 ) with the values of the options, we find that Option 1 ( 2 0 + 2 1 ) is equal to 3 .
Conclusion Therefore, the expression 2 0 + 2 1 is equal to 5 0 + 2 1 .
Examples
Understanding exponents is crucial in many real-world scenarios, such as calculating compound interest. For example, if you invest 100 a t anann u a l in t eres t r a t eo f 5 t ye a rs i s g i v e nb y A = 100(1 + 0.05)^t$. This formula uses exponents to determine the growth of your investment over time. Similarly, exponents are used in calculating population growth, radioactive decay, and many other scientific and financial applications.
The expression 5 0 + 2 1 evaluates to 3, which is equal to option A 2 0 + 2 1 , also evaluating to 3. All other options evaluate to different values. Therefore, the correct answer is option A.
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