Problem 38 - Algebra 1: Concepts and Skills

Question

Use a calculator to evaluate the power. $$ 6^{6} $$

Step-by-Step Solution

Answer

The result of evaluating the power \(6^6\) is 46656.

Step 1: Identify the Base and the Exponent

Here in this exercise, \(6^6\), the base is the number \(6\) and the exponent is also \(6\). This means that we will multiply \(6\) six times.

Step 2: Use Calculator to perform the operation

Now, use a calculator to perform the operation. Input the base number \(6\) and then use the power button (often displayed as ^) followed by the exponent number \(6\). Press equals (=) to get the result.

Key Concepts

Base and Exponent

When working with exponentiation, understanding the terms "base" and "exponent" is crucial. In a power like \(6^6\), the number \(6\) that is repeated as a factor is known as the base.
The exponent, which is also \(6\) in this case, indicates how many times the base is used as a factor. So, \(6^6\) means you multiply \(6\) by itself six times:

• 1st multiplication: \(6 \times 6 = 36\)
• 2nd multiplication: \(36 \times 6 = 216\)
• 3rd multiplication: \(216 \times 6 = 1296\)
• 4th multiplication: \(1296 \times 6 = 7776\)
• 5th multiplication: \(7776 \times 6 = 46656\)
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Knowing how to identify the base and exponent helps you understand what calculation needs to be performed, which is the foundation of evaluating powers.

Using a Calculator

Using a calculator to solve exponentiations makes it quick and easy. Modern calculators often have a specific button for powers, usually labeled as "^" or sometimes "EXP". Here’s a quick guide on how to input an expression like \(6^6\):
- First, input the base number, which is \(6\).- Press the power button "^".- Enter the exponent, which is again \(6\).- Hit the equals "=" button to get the result.
Using a calculator is especially useful for bigger numbers or higher exponents where manual calculation could be cumbersome and error-prone. This not only saves time but also ensures accuracy.

Evaluating Powers

Evaluating powers involves calculating the result when a base raised to an exponent. The formula for calculating powers is written as \(b^e\), where \(b\) is the base and \(e\) is the exponent. For \(6^6\), instead of multiplying manually, a scientific calculator efficiently handles these computations.
The concept of evaluating powers isn’t just about doing the math. It's about understanding how repeated multiplication works and recognizing patterns. For instance, any number to the power of zero is \(1\), and any number to the power of one is itself.
With practice, you'll become more comfortable recognizing and working with powers. This skill is fundamental in algebra, calculus, and beyond, making it an important part of mathematical literacy.