/*! 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 70 Evaluate each expression. $$ ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 70

Evaluate each expression. $$ 4^{3} $$

Short Answer

Expert verified
The expression \(4^3\) evaluates to 64.

Step by step solution

01

Understand the Expression

We need to evaluate the expression \(4^3\). This implies calculating the power, where 4 is the base, and 3 is the exponent.
02

Calculate the Power

The expression \(4^3\) means we are multiplying the base 4 by itself for a total of three factors. Therefore, it can be expanded to \(4 \times 4 \times 4\).
03

Multiply the Factors

First, multiply the first two numbers: \(4 \times 4 = 16\). Then multiply the result with the third number: \(16 \times 4 = 64\).
04

State the Final Result

Thus, the evaluation of \(4^3\) results in 64.

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.

Power and Exponentiation
When dealing with powers, the term "exponentiation" refers to the mathematical operation involving powers. In simple terms, it is a shorthand method to represent repeated multiplication of the same number.
For example, instead of saying "multiply 4 by itself 3 times," we say "4 raised to the power of 3" or just "4 cubed."
The expression is written as \(4^3\), where the number at the bottom (4) is the base, and the small number above it (3) is the exponent.
  • Exponents indicate how many times the base is used as a factor.
  • Exponentiation simplifies expressions and calculations.
Understanding exponentiation is vital in math because it compactly expresses numbers and facilitates calculations, especially in algebra and beyond.
Base and Exponent
In an expression like \(4^3\), the base and the exponent are two key components. The base is the larger number written at the bottom (4 in this case), and it tells you what number is being multiplied.
Meanwhile, the exponent is the smaller number written at the top right corner (3 here) and indicates the number of times the base is multiplied by itself.
The base can be any number, and the exponent is typically a positive integer, though it can be other values too.
  • The base represents the repeated factor.
  • The exponent shows how frequently the base is multiplied.
For instance, in \(4^3\), the calculation involves three 4's being multiplied. Thus, learning about the base and exponent helps students understand not just multiplication but how numbers grow exponentially.
Multiplication Process
When calculating powers, like \(4^3\), the multiplication process comes into play.
To evaluate \(4^3\), you begin by expanding the expression into a multiplication sentence: \(4 \times 4 \times 4\).
Start with the first two numbers: \(4 \times 4\) gives 16. Then, multiply 16 by the last 4: \(16 \times 4\) results in 64.
  • The process demonstrates step-by-step multiplication.
  • Sequential computing helps avoid mistakes.
Breaking it down into steps not only solves the problem efficiently but also instills a solid understanding of the multiplication involved in exponentiation. With practice, these skills enhance a student's problem-solving abilities in higher mathematics.

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

Twice the sum of a number and six equals three times the sum of the number and four. Find the number.

A student is building a bookcase with stepped shelves for her dorm room. She buys a 48 -inch board and wants to cut the board into three pieces with lengths equal to three consecutive even integers. Find the three board lengths.

The sum of \(\frac{2}{3}\) and four times a number is equal to \(\frac{5}{6}\) subtracted from five times the number. Find the number.

The human eye blinks once every 5 seconds on average. How many times does the average eye blink in one hour? In one 16 -hour day while awake? In one year while awake?

A golden rectangle is a rectangle whose length is approximately 1.6 times its width. The early Greeks thought that a rectangle with these dimensions was the most pleasing to the eye and examples of the golden rectangle are found in many early works of art. For example, the Parthenon in Athens contains many examples of golden rectangles. Mike Hallahan would like to plant a rectangular garden in the shape of a golden rectangle. If he has 78 feet of fencing available, find the dimensions of the garden.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure 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.