Problem 53 - Algebra 1

Question

Use a calculator to evaluate the power. For keystroke help see Student Help box on page 11. $$ 6^{8} $$

Step-by-Step Solution

Answer

Calculating the power of 6 raised to 8 using a calculator, the result is \(1679616\).

Step 1: Identify the base and the exponent

In the exercise, the base is 6 and the exponent is 8. The problem is asking us to calculate \(6^{8}\). To do this, we will use a calculator.

Step 2: Input the values in the calculator

First, input the base, which is number 6 in our calculator. Then find the 'power' or 'exponentiation' button on the calculator, usually represented as '^’. After pressing it, input the exponent, which is 8 in this case.

Step 3: Calculate the result

After correctly inputting the base and exponent into the calculator, press the 'equals' button and the calculator should provide us with the result \(1679616\).

Key Concepts

Calculator Techniques

Using a calculator to evaluate expressions is a handy skill, especially when dealing with large numbers or complex calculations.
For powering numbers, most scientific calculators simplify this process by providing a dedicated button, often labeled as "^", "EXP", or "yx".
Here's how you typically use these buttons:

• First, input the base number, which is the number that will be repeatedly multiplied.
• Next, locate and press the exponentiation button.
• Finally, input the exponent number, which tells you how many times to multiply the base by itself.

Once these steps are completed, press the "=" or "Enter" key to compute the power and see the result. This straightforward process saves time and ensures accuracy in your calculations.

Powers in Mathematics

Powers, also known as exponents, are a fundamental concept in mathematics that describe how many times a number, known as the base, is multiplied by itself. For example, in the expression \(6^8\), the number 6 is the base, and 8 is the exponent.
This notation helps simplify longer multiplication expressions. Instead of multiplying 6 by itself eight times, you just express it as \(6^8\).
Understanding powers is crucial, as they often appear in various areas of math and science, such as algebra, physics, and computer science. This concept allows us to work efficiently with very large or very small numbers, especially when combined with technology like calculators.

Base and Exponent Identification

Being able to identify the base and the exponent in expressions is an essential skill in mathematics. It sets the foundation for carrying out operations like exponentiation.
In the expression \(6^{8}\):

• The base is 6. It is the number that is going to be multiplied.
• The exponent is 8. This tells us that 6 should be multiplied by itself a total of eight times.

Recognizing these components helps break down complex expressions into manageable steps, making the problem-solving process simpler. This identification is the first step in performing operations such as evaluating powers using a calculator. It is also a stepping stone for understanding more advanced mathematical operations.