Problem 52 - Algebra 1

Question

Use a calculator to evaluate the power. For keystroke help see Student Help box on page 11. $$ 12^{7} $$

Step-by-Step Solution

Answer

The result of the operation \(12^{7}\) is 35831808.

Step 1: Input Base

Start by inputting '12,' the base, into your calculator.

Step 2: Input Power Operation

Next, find the button on your calculator that indicates the power operation. It may appear as '^' on your calculator. Input the power operation into the calculator following the base number.

Step 3: Input Exponent

After you've put the power operation, input '7,' the exponent.

Step 4: Evaluate

Finally, press the '=,' or the corresponding button on your calculator to evaluate the operation. The calculator will provide the result.

Key Concepts

Calculator Usage

Using a calculator is a practical skill that simplifies complex calculations. When you need to evaluate a power such as \( 12^7 \), a calculator can do the heavy lifting. Here are some general steps and tips for using a calculator for exponentiation:

• Start by ensuring your calculator is in the correct mode for arithmetic operations. Some calculators have different modes for various functions.
• Identify and familiarize yourself with the key that performs exponentiation, commonly labeled as '^' or sometimes 'EXP' on your calculator.
• Once comfortable with the keys, input the base number followed by the exponent.
• Always double-check the entered operations and numbers to prevent errors.

Taking the time to understand how to operate your calculator will make solving math problems more efficient and accurate.

Base and Exponent

The concepts of base and exponent are fundamental to understanding exponentiation. In the expression \( 12^7 \):

• '12' is the base, which is the number we multiply.
• '7' is the exponent, indicating how many times the base is used as a factor.

Think of exponentiation as repeated multiplication. It’s a concise way to express the multiplication of the same number several times.
For example, \( 12^7 \) means multiplying 12 by itself 7 times:
\[ 12 \times 12 \times 12 \times 12 \times 12 \times 12 \times 12 \]
Understanding this makes it easier to comprehend the steps taken when evaluating powers using a calculator.

Mathematical Operations

Mathematical operations form the basis of problem-solving in math. Exponentiation, like \( 12^7 \), is one of these operations. Here is why it's essential:

• Exponentiation is used to represent repeated multiplication, making complex multiplications more manageable.
• It appears in various fields, from calculating compound interest to understanding scientific phenomena like growth rates.
To efficiently work with these operations on a calculator, practice identifying and utilizing the appropriate keys for each operation.
Evaluating powers involves combining knowledge of arithmetic operations with calculator skills, such as correctly entering numbers and operations.
By practicing these skills and understanding the elements of mathematical operations, tasks like evaluating \( 12^7 \) become straightforward.