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Chapter 1: Problem 12

Evaluate. $$ 8^{2} $$

Short Answer

Expert verified
64

Step by step solution

01

Understand the notation

The notation \(8^2\) means 8 raised to the power of 2, also known as 8 squared.
02

Multiply the base by itself

To square a number, multiply it by itself. So, calculate \(8 \times 8\).
03

Perform the multiplication

Calculate the product: \(8 \times 8 = 64\). This is the value of \(8^2\).

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Key Concepts

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

squared numbers
Squared numbers are a type of exponentiation where the exponent is 2. This notation, like in the example \(8^2\), signifies that a number is multiplied by itself. To understand 'squared numbers,' consider it as finding the area of a square. The side length of the square is the base, and the squared number represents its area. So, if each side of a square is 8 units, then the area (or \(8^2\)) will be 64 square units. Using squared numbers simplifies writing and calculating multiplication for numbers multiplying by themselves.
multiplication
Multiplication is a fundamental arithmetic operation that is essentially repeated addition. In the context of exponents, multiplication helps us scale numbers quickly. When we see \(8^2\), it means we perform the multiplication of 8 by itself. Multiplying two numbers involves grouping a certain number of objects into equal-sized groups. Here, 8 groups of 8 objects make 64 objects in total. Practice with simple multiplication can make handling exponents a lot easier, as it is the basis for understanding more complex mathematical functions.
exponentiation
Exponentiation is a mathematical operation that raises a base number to a given power. The notation \(a^n\) signifies a base \(a\) raised to an exponent \(n\), where \(n\) tells how many times to multiply the base by itself. For instance, \(8^2\) involves multiplying 8 by itself once, resulting in 64. Exponentiation simplifies representing and calculating large numbers and is foundational in algebra, geometry, and even computer science. Understanding exponentiation allows you to work with squared numbers, cubes, and higher powers seamlessly.

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