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Chapter 10: Problem 520

Simplify. $$6^{3}$$

Short Answer

Expert verified
216

Step by step solution

01

Understand The Problem

The task is to simplify the expression involving an exponent: \(6^{3}\). This means 6 raised to the power of 3.
02

Write The Expression In Expanded Form

Expand \(6^{3}\) to understand what it means in terms of multiplication: \(6^{3} = 6 \times 6 \times 6\). This means multiplying 6 by itself three times.
03

Perform The Multiplication

First, multiply the first two 6's together: \(6 \times 6 = 36\). Then, multiply the result by the remaining 6: \(36 \times 6 = 216\).
04

Write The Simplified Result

After performing the multiplication, the simplified result of \(6^{3}\) is 216.

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Key Concepts

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

Simplifying Exponents
Understanding how to simplify exponents is essential in math. When we see an exponent like \(6^{3}\), it's telling us to multiply the base number, which is 6, by itself a certain number of times. Here, \(6^{3}\) means we multiply 6 by itself three times:
\[6 \times 6 \times 6 = 216.\]
This step-by-step approach makes it easier to understand and solve problems involving exponents.
Multiplication
Multiplication is one of the fundamental arithmetic operations. In our problem, we used multiplication to expand and simplify \(6^{3}\). Let's look at the multiplication steps more closely:
  • First, we multiplied the first two 6s together: \(6 \times 6 = 36.\)
  • Next, we took the result, 36, and multiplied it by the last 6: \(36 \times 6 = 216.\)
Each multiplication step is simple, but doing them in order simplifies the whole expression.
Arithmetic Operations
Arithmetic operations include addition, subtraction, multiplication, and division. In the exercise, we focused on multiplication to handle the exponents. It's important to follow the correct sequence of arithmetic operations:
  • First, we expanded \(6^{3}\) into multiplication form: \(6 \times 6 \times 6.\)
  • Then, we handled the multiplication step by step to reach the final answer.
Understanding and applying these operations correctly helps to simplify and solve complex mathematical expressions.

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Most popular questions from this chapter

Factor the greatest common factor from each polynomial. $$6 p^{2}+6 p$$

Divide the monomials. $$\frac{28 a^{9} b}{7 a^{4} b^{3}}$$

Multiply the binomials using various methods. $$(2 y-9)(5 y-7)$$

Simplify each expression. $$\left(-\frac{3}{4}\right)^{3}$$

Simplify each expression. $$\frac{x^{4}}{x^{-5}}$$
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