Question

Evaluate by hand. $$ \frac{6-4^{2} \div 2^{3}}{3-4} $$

   Evaluate by hand.
$$
\frac{6-4^{2} \div 2^{3}}{3-4}
$$

College Algebra with Modeling and Visualization

College Algebra with Modeling and Visualization

Gary K. Rockswold 4th Edition

Chapter 1, Problem 22

Instant Answer

Solved by Expert Rishabh Mittal

04/14/2021

Step 1

According to the order of operations (PEMDAS/BODMAS), we should perform the exponentiation and division operations first. So, we have: $$ \frac{6-4^{2} \div 2^{3}}{3-4} $$ becomes $$ \frac{6-16 \div 8}{3-4} $$ Show more…

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Evaluate by hand. $$ \frac{6-4^{2} \div 2^{3}}{3-4} $$

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Key Concepts

Arithmetic_Expression_Simplification

This concept involves systematically reducing a complex expression to its simplest form by applying the correct order of operations. It requires careful evaluation of each component within the expression, such as parentheses and exponents, to arrive at a single numerical value.

Division

Division is a basic arithmetic operation that involves splitting a number into equal parts. It is performed following exponentiation according to the rules of order of operations, and it plays a critical role in accurately simplifying expressions.

Order_of_Operations

This refers to the set of rules that dictatethe sequence in which operations should be performed in a mathematical expression. It ensures consistency in evaluating expressions and is commonly remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Exponentiation

Exponentiation is the mathematical operation involving raising a number to a power. This operation must be carried out according to the order of operations before handling multiplication, division, addition, or subtraction in an expression.

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