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Chapter 5: Problem 135

Evaluate. $$ 4+x^{3}, \text { for } x=10 $$

Short Answer

Expert verified
1004

Step by step solution

01

Identify the given expression and variables

Given the expression to evaluate: 4 + x^3.The variable provided is x, and its value is given as x = 10.
02

Substitute the given value into the expression

Replace the variable x in the expression with the given value: 4 + (10)^3.
03

Calculate the exponents

Calculate the value of the exponent: (10)^3 equals to 10 * 10 * 10 = 1000.
04

Perform the addition

Add the result of the exponentiation to the constant term: 4 + 1000 = 1004.

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Key Concepts

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

Substitution
In mathematics, substitution is the process of replacing a variable with a specific value. This is usually the first step in evaluating an expression. For example, in the given problem, the expression is \(4 + x^3\) and we know that \( x = 10 \).
  • Step 1: Identify the variable in the expression
  • Step 2: Replace the variable with the given value
After the substitution, the expression changes to \(4 + (10)^3\).
Exponents
Exponents are a way to represent repeated multiplication. For instance, \( x^3 \) means multiplying \( x \) by itself three times. In this problem, we need to evaluate \( 10^3 \).
Here's how you can do it:
  • Write down the base number, which is 10.
  • Multiply the base by itself, as many times as the exponent indicates. For \( 10^3 \), multiply 10 three times.
So, \( 10^3 = 10 * 10 * 10 = 1000 \).Reaching this result is essential before moving to the next step.
Addition
Addition is one of the most basic arithmetic operations. It combines two numbers into a single sum. In this example, we need to add the result of our exponent calculation to the constant.
When we have \( 4 + 1000 \):
  • Start by placing the constant 4.
  • Add 1000 to 4.
So, \( 4 + 1000 = 1004 \).This process completes the evaluation of the expression.

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