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Chapter 0: Problem 1

Compute the numbers. $$3^{3}$$

Short Answer

Expert verified
27

Step by step solution

01

Understand the Expression

The given expression is a power of three: \(3^3\). This means that the base number 3 is raised to the power of 3.
02

Expand the Expression

Rewrite the expression in a more detailed form to understand what it represents: \(3^3 = 3 \times 3 \times 3\).
03

Perform the Multiplication

First, multiply the first two 3's: \(3 \times 3 = 9\). Then, multiply the result by the remaining 3: \(9 \times 3 = 27\).

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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 refer to a number being multiplied by itself a certain number of times. In the expression given \(3^3\), the number 3 is known as the 'base', and the number 3 in the exponent position is the 'power' or 'exponent'. The exponent tells us how many times to multiply the base by itself. For instance, in this case, \(3^3\) means multiplying the number 3 by itself three times: \(3 \times 3 \times 3\). Exponentiation helps in simplifying repeated multiplication and is a key concept in algebra and many other areas of math.
multiplication
Multiplication is one of the four fundamental arithmetic operations. It is essentially a shortcut for repeated addition.
For example, instead of adding 3 three times like this: 3 + 3 + 3, we use multiplication, so \(3 \times 3 \times 3\).
In our exercise, breaking it down we first do \(3 \times 3 = 9\).
Then we further multiply this result by 3 again: \(9 \times 3\).
This gives us 27, which is the final answer.
Understanding how to multiply multiple numbers together is crucial for solving more complex mathematical problems efficiently.
basic arithmetic
Basic arithmetic serves as the foundation for all higher-level math. It involves basic operations like addition, subtraction, multiplication, and division. In our exercise, we use multiplication, a core component of arithmetic. By mastering these basic operations, you can tackle a variety of mathematical problems with ease. Let's recap the steps in our exercise:
  • Identify the base (3) and the exponent (3).
  • Expand the expression: \(3^3 = 3 \times 3 \times 3\).
  • Perform the multiplication step-by-step to find the final result (27).
Remember, having a strong grasp of basic arithmetic makes learning advanced math concepts much easier.

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Most popular questions from this chapter

Let \(f(x)=\frac{x}{x-2}, g(x)=\frac{5-x}{5+x},\) and \(h(x)=\frac{x+1}{3 x-1} .\) Express the following as rational functions. $$g\left(\frac{1}{u}\right)$$

Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. $$\sqrt{1+x}(1+x)^{3 / 2}$$

Evaluate \(f(4)\). $$f(x)=x^{3 / 2}$$

Let \(f(x)=x^{6}, g(x)=\frac{x}{1-x},\) and \(h(x)=x^{3}-5 x^{2}+1 .\) Calculate the following functions. $$f(g(x))$$

Find the zeros of the function. (Use the specified viewing window.) $$f(x)=\sqrt{x+2}-x+2 ;[-2,7] \text { by }[-2,4]$$
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