Problem 57 Simplify. $$ 2^{4}+2^{3}-10 ... [FREE SOLUTION]

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Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 10: Problem 57

Simplify. $$ 2^{4}+2^{3}-10 $$

Short Answer

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Step by step solution

Evaluate the Exponents

Calculate the values of the exponents. Start with 2 raised to the power of 4, which is $ 2^4 $, and 2 raised to the power of 3, which is $ 2^3 $. $ 2^4 = 16 $ $ 2^3 = 8 $

Substitute the Results

Substitute the results back into the expression to replace the exponents with their evaluated values. The expression $ 2^4 + 2^3 - 10 $ becomes: $ 16 + 8 - 10 $

Perform the Addition

First, perform the addition in the expression. Add 16 and 8. $ 16 + 8 = 24 $

Perform the Subtraction

Next, perform the subtraction. Subtract 10 from 24. $ 24 - 10 = 14 $

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Exponents

Exponents are a shorthand way of expressing repeated multiplication of the same number. For example, the expression $ 2^4 $ means multiplying 2 by itself 4 times: 2 * 2 * 2 * 2 = 16.
Similarly, $ 2^3 $ means multiplying 2 by itself 3 times: 2 * 2 * 2 = 8.
When faced with expressions that include exponents, the first step is to evaluate (or calculate) the exponent values before doing any other operations.
This helps simplify the expression early on, making the subsequent steps easier to manage. In our exercise, we simplified $ 2^4 $ to 16 and $ 2^3 $ to 8.

Basics of Addition

Addition is one of the primary operations in arithmetic and involves combining two or more numbers to find their total.
In our simplified expression, we have 16 + 8 - 10. Start with the addition part: 16 + 8.
When adding, we combine the two numbers. Here, 16 + 8 gives us 24. This puts us another step closer to simplifying the whole expression.
Understanding and correctly performing addition is crucial for simplifying more complex expressions later on. Always ensure you complete all multiplication and exponent simplifications before moving on to addition.

Steps of Subtraction

Subtraction, the opposite of addition, involves taking one number away from another. In our expression simplify, after adding 16 and 8 to get 24, we need to subtract 10.
So, 24 - 10 = 14.
It鈥檚 important to perform subtraction as one of the final steps when simplifying expressions, since addition and multiplication operations generally take precedence.
By keeping these arithmetic rules in mind, you ensure that you simplify expressions in the correct order and obtain accurate results.

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91影视

Simplify. $$ 2^{4}+2^{3}-10 $$

Short Answer

Step by step solution

Evaluate the Exponents

Substitute the Results

Perform the Addition

Perform the Subtraction

Key Concepts

Understanding Exponents

Basics of Addition

Steps of Subtraction

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