Problem 35 - Algebra 1: Concepts and Skills

Question

Use a calculator to evaluate the power. \(13^{5}\)

Step-by-Step Solution

Answer

The result of evaluating \(13^{5}\) is 371293.

Step 1: Understand the Problem

To solve this exercise, it is crucial to understand what the power of a number means. Here, \(13^{5}\) means multiplying 13 by itself 5 times.

Step 2: Use the Calculator

Enter \(13^{5}\) into the calculator. This operation should result in a single numerical value.

Step 3: Record the Answer

The calculator will provide the answer, which is the result of multiplying 13 by itself 5 times. Write down this number as the solution to the problem.

Key Concepts

calculator use

Using a calculator for evaluating powers can save a lot of time and effort, especially with large exponents. Calculators designed for scientific use have specific buttons and functions to handle exponentiation directly.
When using such a calculator, look for the button labeled "^" or sometimes "yx." This is the exponentiation function.

• First, enter the base number, in our case, 13.
• Next, press the exponentiation button.
• Then, input the exponent, which is 5 in this problem.

Finally, press the equals sign or "enter" to see the result. This ensures that the calculation is done correctly, offering a rapid solution to complex exponentiation tasks.

exponentiation

Exponentiation is a fundamental concept in mathematics where a number known as the base is raised to the power of an exponent. This represents repeated multiplication.
For instance, in the expression \(13^5\), the base is 13, while the exponent, 5, dictates that 13 should be multiplied by itself five times.
Thus,

• First, calculate \(13 \times 13 = 169\).
• Then, multiply 169 by 13 again, which equals 2197.
• Continue multiplying by 13 until you reach the fifth instance of multiplication.

Exponentiation grows quickly in size, which is why calculators are convenient for such computations. By understanding this process, it becomes easier to set up problems correctly whether done manually or with a calculator.

problem-solving skills

Developing problem-solving skills in mathematics requires breaking down problems into manageable steps. In our task of evaluating \(13^{5}\) with a calculator, the ability to identify the right steps is crucial.

• Start by understanding the mathematical operation required, which is exponentiation here.
• Use tools that simplify the task, like a calculator.
• Verify your result by checking for any entry errors or by understanding how the calculation unfolds: 13 multiplied by itself five times.

Effective problem-solving means not just arriving at the answer but knowing how and why the method works. Cultivating these skills helps students tackle a wide range of mathematical challenges confidently.