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Chapter 2: Problem 35

Write in expanded form. \(5^{3}\)

Short Answer

Expert verified
5 \times 5 \times 5

Step by step solution

01

Understand the Exponent

The exponent in the expression \(5^{3}\) indicates that the base number 5 is multiplied by itself a total of 3 times.
02

Write the Multiplication

Write the base number 5, multiplied by itself as many times as indicated by the exponent. In this case, it is: \(5 \times 5 \times 5\).
03

Simplify

Evaluate the multiplication: \(5 \times 5 = 25\), then \(25 \times 5 = 125\).

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Key Concepts

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

Exponents
In mathematics, an exponent indicates how many times a number, known as the base, is multiplied by itself. In the expression \(5^3\), the exponent is 3, meaning the base number 5 is used as a factor three times. Understanding exponents helps us simplify expressions and perform calculations more efficiently. Exponents are widely used in various fields such as algebra, physics, and computer science.
Multiplication
When we deal with exponents, we often need to perform multiple multiplication operations. For instance, \(5^3\) can be expanded to \(5 \times 5 \times 5\). Each multiplication step should be tackled methodically to avoid errors.
  • First, multiply the base number by itself for the count indicated by the exponent.
  • Here, multiply 5 by itself three times (\(5 \times 5 \times 5\)).
  • This step-by-step approach helps to break down complex exponentiation problems.
Simplification
The final step is to simplify the multiplication expression we derived. This means calculating the product of the numbers. For \(5^3 = 5 \times 5 \times 5\):
  • First, multiply 5 by 5 to get 25.
  • Next, multiply the result (25) by 5 again to get 125.

Simplification is crucial to get the final value of the expression. In this case, the expanded form of \(5^3\) simplifies to 125.

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Most popular questions from this chapter

Write in expanded form. \(8^{3}\)

In the following exercises, find the least common multiple of each pair of numbers. $$ 25,35 $$

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