/*! 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 1 Evaluate each expression. See Ex... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 1

Evaluate each expression. See Example 1. $$ 7^{2} $$

Short Answer

Expert verified
The value of \( 7^2 \) is 49.

Step by step solution

01

Understand the Expression

The expression given is \( 7^2 \). This represents the number 7 raised to the power of 2, which means multiplying 7 by itself.
02

Calculate the Power

To calculate \( 7^2 \), you simply multiply 7 by 7. So it will be: \[ 7 \times 7 = 49 \].

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 of a Number
Understanding the power of a number is crucial when working with exponents. An exponent, or the power, indicates how many times a number is multiplied by itself. For instance, when you see an expression like \( 7^2 \), it indicates that 7, which is the base, is used as a factor twice because the exponent is 2.

Let's break it down further:
  • The base is the number that gets multiplied.
  • The exponent, or power, shows how many times to multiply the base by itself.
So, in essence, \( 7^2 \) means to multiply 7 by itself, resulting in 7 times 7. This concept of exponentiation allows you to express large repeated multiplications succinctly and conveniently.
Multiplication
Multiplication is a fundamental arithmetic operation that forms the backbone of working with exponents. When calculating expressions like \( 7^2 \), multiplication is essential because it defines how you approach the expression.

The expression \( 7^2 \) tells us we need to multiply 7 by itself. A simple multiplication setup helps to compute the power effectively:
  • Take the first 7, the base, as shown in the expression.
  • Multiply it by another 7, as many times as indicated by the exponent.
Therefore, when you calculate \( 7 \times 7 \), you translate the expression into its full expanded form, which in this case, results in 49. Understanding multiplication ensures you grasp how exponents multiply a base repeatedly, solidifying foundational math skills.
Step-by-Step Solution
Following a step-by-step approach helps in systematically tackling mathematical expressions, especially those involving exponents. Take the problem of evaluating \( 7^2 \) as an example for understanding how to break down and solve similar tasks.

Here's a simple breakdown:
  • Step 1: Looking at the expression \( 7^2 \) means you're going to multiply 7 by itself, as the exponent is 2.
  • Step 2: Carry out the multiplication calculation \( 7 \times 7 \), which equals 49.
Each step in solving such expressions involves a clear understanding and execution of multiplication. Breaking down problems into smaller parts makes learning manageable and reinforces the basic principles, ensuring clarity and confidence as you work through more complex arithmetic challenges.

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

Simplify each polynomial by combining like terms. $$ 1.85 x^{2}-3.76 x+9.25 x^{2}+10.76-4.21 x $$

Divide If the divisor contains 2 or more terms, use long division. $$ \frac{3 x^{3}+11 x+12}{x+4} $$

Perform the indicated operations. $$(2 x-1)+(10 x-7)$$

Match each expression on the left to the equivalent expression on the right. See the Concept Check in this section. $$ (a+b)^{2}(a-b)^{2} $$ $$A. a^{2}-b^{2}$$ $$B. a^{2}+b^{2}$$ $$C. a^{2}-2 a b+b^{2}$$ $$D. a^{2}+2 a b+b^{2}$$ $$E. none of these$$

Divide If the divisor contains 2 or more terms, use long division. $$ \frac{y^{3}+3 y^{2}+4}{y-2} $$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

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.