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Chapter 1: Problem 16

Find the value of each exponential expression. $$ 11^{3} $$

Short Answer

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Step by step solution

01

Understand the Problem

The task requires finding the value of the exponential expression \(11^{3}\).
02

Write Down the Exponentiation

We need to calculate \(11^{3}\). This means 11 multiplied by itself three times, which can be written as \(11 \times 11 \times 11\).
03

Perform the Multiplication

First, calculate \(11 \times 11 = 121\). Next, multiply the result by 11 again: \(121 \times 11 = 1331\).
04

Write the Final Answer

The value of \(11^{3}\) is 1331.

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Key Concepts

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

Exponentiation
Exponentiation is a mathematical operation involving a base and an exponent. In our exercise, the problem was to find the value of the exponential expression \(11^{3}\).
The base is the number 11, and the exponent is 3. This tells us how many times to multiply the base by itself. For example, \(11^{3}\) means multiplying 11 by itself three times: \(11 \times 11 \times 11\).
The expression \(a^{b}\) means that 'a' is the base and 'b' is the exponent. The result of exponentiation gives us the power of the base.
Multiplication
Multiplication is one of the four elementary mathematical operations. It involves finding the total of one number added repeatedly.
When we multiply, for example, 11 by 11, we are adding 11 to itself 11 times: \(11 \times 11 = 121\).
In our problem, we further multiplied the intermediate result by the base again: \(121 \times 11 = 1331\). This second multiplication completes the operation required for \(11^{3}\).
Multiplication used in exponentiation simplifies the process of repeatedly adding the same number, making complex calculations manageable.
Algebraic Calculations
Algebraic calculations involve operations with numbers and variables using the rules of arithmetic and algebra.
In our step-by-step solution, we applied these rules to solve \(11^{3}\) step-by-step:
  • First, we understood and noted the expression as \(11 \times 11 \times 11\).
  • We performed the intermediate multiplication: \(11 \times 11 = 121\).
  • Next, we multiplied the result by 11 again: \(121 \times 11 = 1331\).
  • Finally, we concluded with the value of \(11^{3} = 1331\).
Applying these step-by-step rules ensures accuracy and helps in understanding the problem-solving process.
Understanding algebraic calculations can simplify solving complex mathematical problems involving exponentiation and multiplication.

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