Problem 53 Evaluate each expression. $$ ... [FREE SOLUTION]

Chapter 1: Problem 53

Evaluate each expression. $$ (9-3)(9-9)^{2} $$

Short Answer

Expert verified

The value of the expression is 0.

Step by step solution

Evaluate the Subtraction Inside the Parentheses

Start by evaluating the expression inside each set of parentheses.First, calculate:$9 - 3 = 6$ Then, calculate:$9 - 9 = 0$

Evaluate the Exponentiation

Now, calculate the exponentiation in the expression.Since we have the expression $(9-9)^2 = 0^2$, perform the exponentiation:$0^2 = 0$

Multiply the Results

Now, substitute the results from Steps 1 and 2 into the expression and perform the multiplication:$(6)(0)$Since any number multiplied by zero is zero, the result is:$6 \times 0 = 0$

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Key Concepts

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

Order of Operations

Understanding the order of operations is crucial when evaluating algebraic expressions. It ensures that everyone solves an expression the same way. The rules for the sequence are often remembered by the acronym PEMDAS:

Parentheses first
Exponents (ie. powers and square roots, etc.)
Multiplication and Division (left-to-right)
Addition and Subtraction (left-to-right)

You always start by solving operations inside parentheses first. In our example:\[ (9-3)(9-9)^2 \]Inside the parentheses, you first perform the subtraction:\[ 9-3\] and \[9-9\]This simplifies into:\[ 6(0)^2 \]By following the order of operations, you stay on the correct path to find the right answer.

Exponentiation

Exponentiation is the process of raising a number to a power. It answers how many times a number, the base, is multiplied by itself. For example, in the expression:\[ (9-9)^2 \]The exponent is 2, meaning that you multiply the base \[ 0 \] by itself:\[ 0^2 = 0 \]Important aspects of exponentiation to keep in mind:

If a number is raised to the power of 2, it is called 'squared'.
Any number raised to the power of 0 is always 1 (but make sure the base isn't 0).
In our example, raising 0 to any power results in 0.

Exponentiation can significantly change values in expressions, which is why it's crucial for finding accurate results.

Multiplication by Zero

Multiplication by zero is a straightforward yet powerful concept in mathematics. It states that any number multiplied by zero results in zero. This is because zero groups of any number equal zero:\[ (6)(0) \]In our given expression, after simplification and exponentiation, you multiply the results. Since:\[ 6 \times 0 = 0 \]The reason is simple:

No matter how big or small a number is, when you multiply it by zero, you have nothing at all.
This rule is consistent across all types of numbers, whether integers, fractions, or even variables.

This principle can simplify complex expressions quickly if zero is detected as a multiplicative factor.

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91影视

Evaluate each expression. $$ (9-3)(9-9)^{2} $$

Short Answer

Step by step solution

Evaluate the Subtraction Inside the Parentheses

Evaluate the Exponentiation

Multiply the Results

Key Concepts

Order of Operations

Exponentiation

Multiplication by Zero

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