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Chapter 4: Problem 29

Simplify. $$ 2^{4} \div 4-2 $$

Short Answer

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Step by step solution

01

- Evaluate the exponent

Calculate the value of the exponent: \( 2^{4} \). This means multiplying 2 by itself four times: \( 2 \times 2 \times 2 \times 2 = 16 \). So, \( 2^{4} = 16 \).
02

- Perform the division

Next, use the result of the exponentiation to perform the division: \( 16 \div 4 \). Dividing 16 by 4 gives \( 16 \div 4 = 4 \).
03

- Perform the subtraction

Finally, subtract 2 from the result of the division: \( 4 - 2 \). This equals \( 4 - 2 = 2 \).

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Key Concepts

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

Exponents
Exponents are a way to represent repeated multiplication of the same number. For example, in the expression \( 2^{4} \), 2 is the base, and 4 is the exponent, which means you multiply the base 2 by itself 4 times: \( 2 \times 2 \times 2 \times 2 \). Understanding exponents is crucial for simplifying mathematical expressions efficiently.

Here are key points to remember about exponents:
  • The base is the number being multiplied.
  • The exponent indicates how many times the base is multiplied by itself.
  • Exponents follow the order of operations (PEMDAS/BODMAS) rules, so they should be evaluated before performing multiplication, division, addition, or subtraction.
In our given exercise, we first evaluate \( 2^{4} \) which results in 16. This simplifies the original expression to \( 16 \div 4 - 2 \).
Division
Division is the process of splitting a number into equal parts. It is one of the four basic operations in arithmetic, alongside addition, subtraction, and multiplication. When you divide, you are essentially finding out how many times one number is contained within another. The symbol for division is \( \div \).

Here鈥檚 a breakdown of division:
  • The number you start with is called the dividend.
  • The number you are dividing by is called the divisor.
  • The result is called the quotient.
In our exercise, we divide 16 by 4 where 16 is the dividend and 4 is the divisor. Performing the division, \( 16 \div 4 \) gives us 4. So, the expression simplifies further to \( 4 - 2 \).
Subtraction
Subtraction is one of the basic arithmetic operations where we take away a certain amount from a number. It is represented by the minus sign (\( - \)). Subtraction shows how much is left after some part is removed from the whole.

Key points about subtraction:
  • The number from which we subtract is called the minuend.
  • The number that is subtracted is called the subtrahend.
  • The result is called the difference.
In the final step of our exercise, we subtract 2 (subtrahend) from 4 (minuend), resulting in a difference of 2.
So, the final answer to the original problem \( 2^{4} \div 4 - 2 \) is 2.

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