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Chapter 2: Problem 447

In the following exercises, evaluate each expression. $$ y^{3} \text { when } y=5 $$

Short Answer

Expert verified
125

Step by step solution

01

Understand the problem

The goal is to evaluate the expression given by the cube of variable y when y equals 5.
02

Substitute y with 5

Replace the variable y with the value 5 in the expression. This changes the expression from y^3 to 5^3.
03

Evaluate the expression

Calculate 5 raised to the power of 3. This is given by 5 * 5 * 5.
04

Calculate

5 * 5 = 25 and then 25 * 5 = 125. Hence, 5^3 = 125.
05

Write the final answer

Thus, the value of y^3 when y equals 5 is 125.

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Key Concepts

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

exponents
An exponent is a mathematical notation indicating the number of times a number, known as the base, is multiplied by itself. For example, in the expression 5^3, 5 is the base and 3 is the exponent. The exponent tells you how many times to multiply the base by itself. So, 5^3 means 5 * 5 * 5, which equals 125. Exponents are a key concept in algebra and are used to simplify expressions and solve equations. They can also be used to represent large numbers in a compact form. Understanding how to work with exponents is essential for mastering more complex mathematical topics.
substitution
Substitution is a method used in algebra to simplify expressions by replacing variables with their actual values. In our exercise, we are given the expression y^3 and are asked to evaluate it when y equals 5. The first step is to substitute y with 5 in the expression. This changes the expression from y^3 to 5^3. Once the substitution is made, you can proceed with evaluating the expression using arithmetic operations. Substitution is a fundamental concept in algebra that allows you to solve equations by simplifying expressions step-by-step.
powers of numbers
The concept of powers of numbers is closely related to exponents. A power of a number is the result of multiplying that number by itself a certain number of times. For example, the power 5^3 means multiplying 5 by itself three times: 5 * 5 * 5, which equals 125. Powers of numbers help in simplifying complex calculations and expressing large numbers concisely. They are used in various fields of science and engineering to model exponential growth, decay, and even in computing powers of binary numbers. Understanding how to calculate and use powers of numbers is essential for tackling advanced mathematical problems.

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