/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 14 Evaluate each expression. See Ex... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 14

Evaluate each expression. See Example 1. $$ 9 \cdot 1^{7} $$

Short Answer

Expert verified
9

Step by step solution

01

Understanding the Power of 1

Recognize that any number raised to the power of 1 is always that number itself. Here, the base is 1 and the exponent is 7, which means you have to multiply 1 by itself 7 times. However, any number to the power of zero is 1, thus, \[1^7 = 1\] because 1 multiplied by itself any number of times is always 1.
02

Multiply 9 by the Result

Now that we know \(1^7 = 1\), we multiply this by 9 as per the original expression:\[9 \cdot 1 = 9\]Thus, the final value of the expression is 9.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Exponentiation
Exponentiation is a mathematical operation that involves two numbers: a base and an exponent. It is often written as a small superscript number to the top right of the base, like this: \( b^n \). The base, \( b \), is the number being multiplied, and the exponent, \( n \), tells you how many times to multiply the base by itself. For example, with \( 1^7 \), the base is 1 and the exponent is 7. This means you multiply 1 by itself 7 times.

In this particular example:
  • The operation simplifies easily, because 1 multiplied by itself any number of times remains 1, represented as \( 1^n = 1 \).
  • This is a unique property of the number 1 in exponentiation, making the calculation straightforward for all positive exponents.
Exponentiation thus helps in simplifying repeated multiplication into concise expressions, which is both efficient and manageable. This is particularly useful when dealing with large numbers and high exponents.
Power of One
Understanding the concept of the "power of one" is crucial for simplifying expressions in mathematics. When you encounter a base of 1 raised to any power, it is always equal to 1. This is because the number 1 is identity for multiplication.

Regardless of the magnitude of the exponent:
  • \( 1^0 \) is 1.
  • \( 1^1 \) is also 1.
  • \( 1^{100} \) will still be 1.
This is because multiplying 1 by itself, any number of times, doesn't change its value. This principle simplifies not just calculations but also understanding how larger expressions can be evaluated quickly. Knowing the power of one helps you immediately identify that portions of expressions involving \( 1^n \) contribute nothing more than themselves during multiplication with other terms.
Multiplication
Multiplication is a fundamental arithmetic operation used to calculate the total of a number being added several times. In its simplest form, it is about combining equal groups of objects together.

In our original expression:
  • The number 9 represents a group size.
  • The result of the power \( 1^{7} \) is 1.
  • Multiplying 9 by 1 doesn't change the value of 9, represented as \( 9 \cdot 1 = 9 \).
Therefore, understanding how to multiply with the identity factor 1 simplifies our tasks. This is rooted in the property that any number multiplied by 1 remains unchanged. Multiplication is often visually depicted using arrays or groups, helping students grasp the concept of adding identical numbers together efficiently, which is an essential skill in math.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Multiply. $$(4 x+5)\left(8 x^{2}+2 x-4\right)$$

Recall that the perimeter of a figure such as the ones shown in \(E x-\) ercises 73 through 76 is the sum of the lengths of its sides. Find the perimeter of each figure. A wooden beam is \(\left(4 y^{2}+4 y+1\right)\) meters long. If a piece \(\left(y^{2}-10\right)\) meters is cut, express the length of the remaining piece of beam as a polynomial in \(y .\) (GRAPH NOT COPY)

Write each number in standard notation. See Example 6 The distance light travels in 1 year is \(9.460 \times 10^{12}\) kilometers. Write this number in standard notation.

Divide If the divisor contains 2 or more terms, use long division. $$ \frac{5-6 x^{2}}{x-2} $$

Divide. $$ \frac{x^{5}+x^{2}}{x^{2}+x} $$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.