Problem 37 - Algebra 1: Concepts and Skills

Question

Use a calculator to evaluate the power. $$ 12^{7} $$

Step-by-Step Solution

Answer

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

Step 1: Understand the problem

We need to calculate \(12^{7}\). This means to multiply 12 by itself 7 times.

Step 2: Perform multiplication

Use a calculator to perform the multiplication. You can type it as 12^7 or 12*12*12*12*12*12*12.

Step 3: Collect and Check the result

The calculator should give a result of 35831808. To check, type in 12*12*12*12*12*12*12 into the calculator. It should also return 35831808.

Key Concepts

Calculator Use in Mathematics

Calculators are invaluable tools in mathematics, especially when dealing with complex or lengthy calculations. They save time and reduce the possibility of human error. When you're working on exponentiation, like in the exercise where we calculated \(12^7\), a calculator can be especially handy.
To use a calculator for exponentiation:

• Locate the exponentiation function, often denoted by a caret (^) or a button labeled 'EXP' or 'power'.
• Input the base number, in this instance, 12.
• Press the exponentiation function key.
• Input the exponent, here 7, and hit 'Enter' or '='.

This sequence allows you to directly compute powers without performing multiple multiplications manually. Calculators help ensure accuracy, so you can be confident in your results.

Basic Arithmetic Operations

Basic arithmetic operations form the foundation of most mathematical problems. They include addition, subtraction, multiplication, and division. When we talk about calculating powers, multiplication is the key arithmetic operation involved. For instance, to manually compute \(12^7\), you would multiply 12 by itself seven times. Here's a simplified breakdown:

• Multiply the first pair: \(12 \times 12 = 144\)
• Then, multiply the result by 12 again: \(144 \times 12 = 1728\)
• Continue this process until you reach the seventh multiplication.

Without a calculator, this would require careful calculation at each step to avoid mistakes. Understanding the role of multiplication in powers aids in grasping how exponentiation magnifies numbers quickly, as it involves repeated operations.

Power of a Number

The concept of the power of a number, or exponentiation, is fundamental in mathematics. It involves multiplying a number, known as the base, by itself a specific number of times indicated by the exponent. In our exercise, the power being calculated was \(12^7\). Here:

• 12 is the base number.
• 7 is the exponent.
• The result, 35831808, is known as the power.

Understanding powers is crucial because they provide a shorthand way to express large numbers. They are widely used in various fields like physics, engineering, computer science, and more. Exponentiation also underpins many algebraic processes, making it a key concept to master for advanced mathematical studies.