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Chapter 2: Problem 38

Evaluate the given expression. $$2^{3} 3^{4}$$

Short Answer

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Step by step solution

01

- Evaluate the power of 2

First, calculate the value of the expression for the base 2 raised to the power of 3. This means we need to evaluate \(2^{3}\). We know that \(2^{3} = 2 \times 2 \times 2 = 8\).
02

- Evaluate the power of 3

Next, calculate the value of the expression for the base 3 raised to the power of 4. This means we need to evaluate \(3^{4}\). We know that \(3^{4} = 3 \times 3 \times 3 \times 3 = 81\).
03

- Multiply the results

Finally, multiply the results from step 1 and step 2. So, we need to multiply 8 (from \(2^{3}\)) by 81 (from \(3^{4}\)). Thus, \(2^{3} \times 3^{4} = 8 \times 81 = 648\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

powers of numbers
When we talk about powers of numbers, we're referring to expressions like \(2^{3}\) or \(3^{4}\). These are also known as 'exponents'. The number that's being multiplied is called the base, and the small number on top is the exponent or power.

For example, in \(2^{3}\), 2 is the base and 3 is the exponent. This means you multiply 2 by itself three times:
  • 2 脳 2 脳 2 = 8
Similarly, in \(3^{4}\), the base is 3 and the exponent is 4. Thus, you multiply 3 by itself four times:
  • 3 脳 3 脳 3 脳 3 = 81
Understanding the concept of powers and exponents is crucial for math problems involving repeated multiplication.
multiplication
Multiplication is one of the basic arithmetic operations. It's all about combining groups of numbers. In the context of our exercise, we're dealing with multiplying results of powers.

Let's break it down:
  • First, we found \(2^{3} = 8\).
  • Next, we calculated \(3^{4} = 81\).
  • Finally, we need to multiply these two results: \(8 \times 81\).
To multiply 8 and 81, you can use traditional methods or tools, but doing it step by step makes it easy. The multiplication of these two numbers gives us 648:
  • 8 脳 81 = 648
Multiplying the results of powers gives us the final value of the original expression.
step-by-step evaluation
Evaluating math expressions step by step helps in breaking down complex problems into manageable parts. Let's walk through how we evaluated the original expression \(2^{3} \times 3^{4}\) in a simpler, understandable way.

Step 1: Calculate \(2^{3}\)
  • Find the value of 2 raised to the power of 3.
  • Multiply 2 by itself three times: \(2 \times 2 \times 2 = 8\).
Step 2: Calculate \(3^{4}\)
  • Find the value of 3 raised to the power of 4.
  • Multiply 3 by itself four times: \(3 \times 3 \times 3 \times 3 = 81\).
Step 3: Multiply the results
  • Finally, multiply the results from step 1 and step 2: \(8 \times 81 = 648\).
By following each of these steps carefully, we make sure we understand how to tackle similar problems in the future. Step-by-step evaluation ensures clarity and accuracy in solving math exercises.

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Most popular questions from this chapter

Simplify by combining like terms whenever possible. $$0.35 x+0.42(2 x)+0.54(80-3 x)$$

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