Problem 55 - Algebra 1

Question

Use a calculator to evaluate $$3^{12}$$

Step-by-Step Solution

Answer

The result of \(3^{12}\) evaluated using a calculator is 531441.

Step 1: Understand the problem

The problem is asking to find the value of the expression \(3^{12}\). Let's use a calculator to solve the power.

Step 2: Use the calculator

Find the button marked '^' on the calculator and then plug in the equation as follows: 3^12.

Step 3: Evaluate the expression

After entering the expression, press the '=' button or 'Enter' to evaluate the expression.

Key Concepts

Calculator Use

Calculators are handy tools that simplify complex mathematical problems. When dealing with exponentiation, they make our job much easier. Knowing how to use a calculator correctly is crucial for accurate results. Begin by familiarizing yourself with the calculator's layout. Most calculators have an operation button specifically for exponentiation, often marked as '^' or '**'.
To calculate a power like $3^{12}$, follow these steps:

• Turn on your calculator.
• Enter the base number, in this case, 3.
• Press the exponentiation button '^'.
• Enter the exponent number, which is 12 here.
• Press '=' or 'Enter' to compute the result.

With practice, using these functions becomes second nature, enhancing your computational efficiency.

Powers of Numbers

The concept of powers of numbers is critical in algebra and involves multiplying a number by itself a certain number of times. The operation can be expressed mathematically as: \[ a^n \] where \( a \) is the base and \( n \) is the exponent. In the case of \( 3^{12} \), the base 3 is multiplied by itself 12 times.
Repeated multiplication can quickly become complex, especially with larger numbers or higher exponents. Calculators offer a quick solution, allowing you to focus on understanding patterns and relationships in mathematics instead of manually working out large computations. Recognizing these patterns can aid in estimating and checking your work for errors.

Mathematical Expressions

Mathematical expressions are combinations of numbers, operations, and sometimes variables or brackets. They represent quantities or relationships and need to be interpreted or evaluated correctly. In our exercise, the expression \( 3^{12} \) is a straightforward type of expression involving exponentiation.
To evaluate an expression:

• Identify the operations to be performed, such as addition, subtraction, multiplication, or exponentiation.
• Follow the order of operations, also known as BODMAS/BIDMAS (Brackets, Orders (i.e., powers and roots), Division and Multiplication, Addition and Subtraction).
• Use a calculator for expressions that are difficult to compute mentally.

Understanding these expressions helps break down complex problems into manageable parts, leading to more accurate solutions.