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Chapter 2: Problem 2

The first step in evaluating \((9-3)^{2}\) is _________ .

Short Answer

Expert verified
The first step in evaluating \((9-3)^{2}\) is performing the subtraction inside the parentheses: \( (9-3) = 6 \).

Step by step solution

01

Subtraction inside the parentheses

Perform the subtraction within the parentheses: \( (9-3) = 6 \)
02

Squaring the result

Now, square the result obtained in step 1: \( 6^{2} = 36 \) So, the first step in evaluating \((9-3)^{2}\) is subtracting 3 from 9 inside the parentheses.

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Key Concepts

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

Parentheses in Mathematics
In mathematics, parentheses \(( )\) are used to group parts of an expression. They indicate which operations should be performed first. For example, in the expression \((9-3)^{2}\), the subtraction inside the parentheses must be done before any other operations. This is because operations inside parentheses are prioritized according to the order of operations.

Why are parentheses important?
  • They help in organizing complex expressions.
  • They ensure operations are performed in the correct order.
  • They can change the outcome of a computation. Without them, different operations might be done first, leading to incorrect results.
Remember, always handle the operations within the parentheses first before moving on to other parts of the equation.
Exponentiation
Exponentiation is the operation of raising one number, called the base, to the power of another number, called the exponent. In an expression like \((a)^n\), \(a\) is the base and \(n\) is the exponent. This means you multiply the base by itself \(n\) times.

In our example \((9-3)^2\), after calculating \(9-3 = 6\), we have an exponentiation to do: \(6^{2}\). This stands for multiplying 6 by itself, which is \(6 \times 6 = 36\).

What to keep in mind with exponentiation:
  • Exponentiation is simplified after completing operations inside parentheses.
  • It is the second step in the order of operations after resolving operations inside parentheses.
  • The exponent tells you how many times to use the base in a multiplication.
Understanding exponentiation helps in tackling more complex mathematical problems with confidence.
Evaluating Expressions
Evaluating expressions involves performing the operations indicated to find a numerical value for a math expression. This process follows the order of operations, typically remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)).

Steps for Evaluating Expressions:
  • First, look for and solve any expressions within parentheses.
  • Next, handle any exponents or powers.
  • Proceed to multiplication and division, from left to right.
  • Finally, address addition and subtraction, from left to right.
In evaluating \((9-3)^{2}\), you would first solve the subtraction \((9-3)\) resulting in \(6\), and then handle the exponent by squaring 6 to get \(36\).

Evaluating expressions accurately ensures clarity and correctness in solving mathematical problems.

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Most popular questions from this chapter

Perform the operation as indicated. Write the final answer without an exponent. \(\left(4.7 \times 10^{-3}\right)+\left(8.8 \times 10^{-3}\right)\)

Simplify the expression using the product rule. Leave your answer in exponential form. $$\left(\frac{8}{21} b\right)\left(-6 b^{8}\right)\left(-\frac{7}{2} b^{6}\right)$$

Simplify the expression using the product rule. Leave your answer in exponential form. $$(-3) \cdot(-3)^{5} \cdot(-3)^{2}$$

Simplify the expression using one of the power rules. $$\left(t^{6}\right)^{7}$$

Simplify using the quotient rule. $$\frac{9 x^{-5} y^{2}}{4 x^{-2} y^{6}}$$
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