Simplify: [tex]14^0+2^7+15^1[/tex]
Answer (2)
Evaluate 1 4 0 , which equals 1.
Evaluate 2 7 , which equals 128.
Evaluate 1 5 1 , which equals 15.
Add the results: 1 + 128 + 15 = 144 . The simplified expression is 144 .
Explanation
Understanding the Problem We are asked to simplify the expression 1 4 0 + 2 7 + 1 5 1 . To do this, we need to evaluate each term separately and then add them together. Let's start by recalling some basic exponent rules.
Evaluating 1 4 0 First, let's evaluate 1 4 0 . Any non-zero number raised to the power of 0 is equal to 1. Therefore, 1 4 0 = 1 .
Evaluating 2 7 Next, let's evaluate 2 7 . This means we need to multiply 2 by itself 7 times: 2 7 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 128 .
Evaluating 1 5 1 Now, let's evaluate 1 5 1 . Any number raised to the power of 1 is equal to the number itself. Therefore, 1 5 1 = 15 .
Adding the Results Finally, let's add the results from the previous steps: 1 4 0 + 2 7 + 1 5 1 = 1 + 128 + 15 = 144 .
Conclusion Therefore, the simplified expression is 144.
Examples
Exponents are used to calculate 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$ years is given by 100 ( 1 + 0.05 ) t . Understanding exponents helps you calculate how your investments grow over time. Also, exponents are used in computer science to calculate memory sizes (e.g., kilobytes, megabytes, gigabytes) and processing power.
To simplify the expression 1 4 0 + 2 7 + 1 5 1 , evaluate each term: 1 4 0 = 1 , 2 7 = 128 , and 1 5 1 = 15 . Adding these values together gives 1 + 128 + 15 = 144 . The final answer is 144 .
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