/*! 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 4 Write each number as a power. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 4

Write each number as a power. 27

Short Answer

Expert verified
The number 27 can be written as \(3^3\).

Step by step solution

01

Recognize the Base

Identify the base that is raised to a power to form the number 27. The common bases to try include small integers like 2, 3, and 5.
02

Experiment with Powers

Try raising the base to different powers to match the given number, 27. Check: \( 3^1 = 3 \) \( 3^2 = 9 \) \( 3^3 = 27 \)
03

Find the Correct Expression

Since \(3^3 = 27\), the number 27 can be written as a power using 3 as the base and 3 as the exponent.

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.

Base and Exponent
When we talk about powers and exponents, two essential components come into play: the base and the exponent. Understanding these elements helps us express numbers more efficiently.
  • Base: This is the number that gets multiplied. It is the main number in an expression, like the number 3 in the expression \(3^3\).
  • Exponent: This tells us how many times to use the base in a multiplication. In \(3^3\), the exponent is 3, indicating that 3 is used three times in multiplication (\(3 \times 3 \times 3\)).
Recognizing the base and exponent is similar to recognizing familiar faces in a crowd. It simplifies the understanding of multiplication repeated multiple times. This is integral to simplifying operations and solving mathematical expressions proficiently.
Exponential Notation
Exponential notation is a shorthand way of expressing repeated multiplication of the same number. It鈥檚 like a language shortcut that turns a long multiplication sequence into a compact form.
  • In exponential notation, \(b^n\), the base \(b\) is multiplied by itself \(n\) times. It's highlighted by looking at \(3^3\), which equals \(3 \times 3 \times 3\).
  • This method makes it easier to perform calculations involving large numbers, and it's especially useful in fields involving mathematics, engineering, and the sciences.
Exponential notation bridges the gap between simplicity and complexity, converting lengthy multiplication into a simple form that鈥檚 easier to manipulate and understand. This notation is an essential mathematical tool.
Power of a Number
Expressing a number as a power involves writing it in the form \(b^n\). This is where you show the relationship between the base, the exponent, and the overall result. For example, the number 27 can be expressed as a power of 3: \(3^3 = 27\). This is because the base (3) is used in a multiplication three times (3 multiplied by itself twice more), resulting in the number 27.
  • To understand the power of a number, break it down to see how many times the base needs to be multiplied to get the final result.
  • This expression helps by simplifying complex equations and providing insight into the behavior of numbers in operations.
The concept of a power helps in recognizing patterns and simplifying calculations, forming a core part of mathematical problem-solving. It's like demonstrating the secret behind a magic trick, revealing its simplicity.

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

In \(74-82,\) write each expression as a power with positive exponents in simplest form. $$ \left(\frac{x^{2} y}{3 x^{4} b^{2}}\right)^{\frac{2}{3}} $$

In \(11-16,\) use the formula \(A=A_{0}\left(1+\frac{r}{n}\right)^{n t}\) to find the missing variable to the nearest hundredth. $$ A=6, A_{0}=36, n=1, t=4 $$

In \(38-57,\) write each radical expression as a power with positive exponents and express the answer in simplest form. The variables are positive numbers. $$ \sqrt{\frac{3 a}{4 b}} $$

In \(3-10,\) find the value of \(x\) to the nearest hundredth. $$ x=e^{-1} $$

In \(3-10,\) find the value of \(x\) to the nearest hundredth. $$ x=e^{3}+e^{5} $$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

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.