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Chapter 0: Problem 53

For exercises 1-80, evaluate. $$ 160-2 \cdot 5 \cdot 3^{2} $$

Short Answer

Expert verified
The answer is 70.

Step by step solution

01

Evaluate the exponent

First, calculate the value of the exponent. Here, we have the term \(3^{2}\). \(3^{2} = 3 \times 3 = 9\)
02

Multiply the results

Next, multiply the results with the remaining terms in the expression. The expression becomes: \(2 \times 5 \times 9\) First multiply \(2 \times 5 = 10\). Then multiply the result by 9, \(10 \times 9 = 90\).
03

Subtract from initial value

Finally, subtract the result from the initial value in the expression: \(160 - 90 = 70\).

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Key Concepts

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

Evaluating Expressions
Evaluating expressions involves performing operations in a specific order to reduce an expression to a single value. This process requires following the 'order of operations', often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

In expressions without parentheses, start with exponents, then proceed to multiplication or division, and finally handle addition or subtraction. By following this order, you ensure the expression is simplified correctly.
Exponents
Exponents represent repeated multiplication of a number by itself. For example, in the exercise provided, we have the term \(3^2\). This means multiplying 3 by itself: \(3 \times 3 = 9\).

Exponents are a critical part of many mathematical expressions and must always be evaluated before any multiplications, divisions, additions, or subtractions. Understanding exponents' basics is key to correctly simplifying expressions.
Multiplication
Multiplication involves combining quantities by multiplying them. In the exercise, the expression \(2 \times 5 \times 9\) is evaluated by performing multiplications in sequence. First, you calculate \(2 \times 5 = 10\). Then multiply this result by 9 to get 90.

Always handle multiplications before moving on to additions or subtractions unless parentheses dictate otherwise. This ensures you maintain the correct order of operations.
Subtraction
Subtraction involves taking one quantity away from another. It is usually performed after all operations within parentheses, exponents, multiplications, and divisions are completed. In our exercise, the final step is to subtract 90 from 160: \(160 - 90 = 70\).

Remember to always follow the order of operations to ensure that the subtraction (and any other operations) are performed at the correct time in the sequence.

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Most popular questions from this chapter

For exercises \(47-58\), rewrite the percent as a decimal number. $$ 18 \% $$

$$ \text { Round } 65,432 \text { to the nearest thousand. } $$

For exercises \(47-58\), rewrite the percent as a decimal number. $$ 3.25 \% $$

If 5 out of 20 shirts are T-shirts, find the percent of the shirts that are T-shirts.

Copy and complete the table. $$ \begin{array}{|c|c|c|} \hline \begin{array}{c} \text { Fraction } \\ \text { notation } \end{array} & \begin{array}{c} \text { Percent } \\ \text { notation } \end{array} & \begin{array}{c} \text { Decimal number } \\ \text { notation } \end{array} \\ \hline \frac{4}{5} & & \\ \hline \frac{61}{100} & 91 \% & \\ \hline & 7 \% & \\ \hline & 311 \% & \\ \hline & & \\ \hline & & \\ \hline & & 0.01 \\ \hline & & \\ \hline & & \\ \hline \end{array} $$
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