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Chapter 5: Problem 11

Identify the base and the exponent in each expression. $$ 8 n^{0} $$

Short Answer

Expert verified
Base is n, exponent is 0.

Step by step solution

01

Identify the Entire Expression

First, look at the whole expression given: 8 n^{0}.
02

Locate the Base in the Expression

In exponential notation, the base is the number or variable that is being raised to a power. In the expression 8 n^{0}, the base is the variable or number being raised to a power.
03

Locate the Exponent

The exponent is the number indicating how many times the base is multiplied by itself. In this case, the exponent is 0.
04

Combine Information

Now that the base and the exponent have been identified: the base is n and the exponent is 0.

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Key Concepts

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

Understanding the Base in Exponential Notation
In exponential notation, the base is the foundational number or variable that gets raised to a power.
To understand this better, consider the expression provided in the exercise: $$8 n^{0}.$$ The base is the variable or the number that is being raised to the exponent. Therefore, in our exercise, the base is $$n.$$ The base is crucial because:
  • It indicates which number or variable is being used in repeated multiplication.
  • It helps in identifying the starting point before applying the exponent.
For example, in $$2^{3},$$ the number $$2$$ is the base, meaning $$2$$ will be multiplied by itself multiple times according to the exponent.
Deciphering the Exponent in Exponential Notation
The exponent is a number that shows how many times the base is to be multiplied by itself.
In the expression $$8 n^{0},$$ the exponent is 0. Here's what you need to remember about exponents:
  • The exponent tells you the power to which the base must be raised.
  • When an exponent is 0 (like in our exercise), any non-zero base raised to the power of 0 is equal to 1.This is a special rule and is very important to remember: $$n^{0} = 1,$$ where $$n e 0$$.
Understanding the exponent helps you control how many times to multiply the base in exponential expressions.
Introduction to Algebra and Its Importance
Algebra is a branch of mathematics that uses letters and symbols to represent numbers and quantities in formulas and equations.
In our exercise, we encounter an algebraic expression like $$8 n^{0}.$$ Here's what makes algebra essential:
  • It allows us to generalize arithmetic relations and operations.
  • We can solve complex problems by setting up equations and manipulating symbols.
Algebra is foundational in mathematics and is used in various fields such as engineering, physics, economics, and more.
Recognizing the base and exponent in expressions is a critical skill in algebra for simplifying and solving complex equations.

Whenever you see an expression like $$n^{0},$$ you now understand that algebra helps us decode it meaningfully.

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Most popular questions from this chapter

Use the fact that \(10^{3} \approx 2^{10}\) to estimate each of the following powers of \(2 .\) Then compute the power of 2 with a calculator and find the difference between the exact value and the approximation. $$ 2^{26} $$

For each pair of functions fand \(g\), determine the domain of the sum, the difference, and the product of the two functions. $$ \begin{aligned} &f(x)=5 x-1\\\ &g(x)=2 x^{2} \end{aligned} $$

To prepare for Section \(5.2,\) review operations with integers (Sections \(1.5-1.7)\) Perform the indicated operations. $$ 12-(-4) $$

Simplify. Assume that no denominator is zero and that \(0^{0}\) is not considered. $$ \left(\frac{-4 p^{8}}{3 m^{2} n^{3}}\right)^{3} $$

To prepare for Section \(5.2,\) review operations with integers (Sections \(1.5-1.7)\) Perform the indicated operations. $$ -3(5) $$
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