/*! 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 74 Evaluate the expression. $$3^{... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 74

Evaluate the expression. $$3^{2} \cdot 4+8$$

Short Answer

Expert verified
The result of the expression \(3^{2} \cdot 4 + 8\) is 44.

Step by step solution

01

Handle Exponents

Compute the part of the expression where exponentiation is used. Here, \(3^{2}\) is equal to 9.
02

Process Multiplication

The next step is to perform the multiplication. Multiply the result from step 1 with 4. So, \(9 \cdot 4 = 36\)
03

Finish with Addition

Having handled the multiplication, the last PEMDAS/BODMAS operation is addition. Now, add the result you got in step 2 with 8. Hence, \(36 + 8 = 44\).

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 involving two numbers, the base and the exponent. In the expression
\(3^{2}\), 3 is the base and 2 is the exponent, and it tells us to multiply 3 by itself 2 times. Thus, \(3^{2} = 3 \times 3 = 9\).
This operation is an essential component of arithmetic and appears in various forms throughout different levels of math. It is crucial to perform exponentiation correctly before moving on to other operations when evaluating expressions.
PEMDAS
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. It is a mnemonic aiding in remembering the order of operations to correctly solve math problems.
When you come across an expression like \(3^{2} \times 4 + 8\), PEMDAS guides you to start with any calculations inside parentheses, then move to exponents, followed by multiplication and division from left to right, and finally addition and subtraction in sequence.
It's important to follow this specific order to ensure the accuracy of your solution.
Multiplication
Multiplication is one of the fundamental arithmetic operations. Simply put, it is repeated addition. For instance, \(9 \times 4\) means adding the number 9 to itself 4 times, resulting in 36.
In algebra, when evaluating expressions, multiplication comes after any parentheses or exponents have been addressed. It's also worth noting that multiplication is commutative, meaning that the order of the numbers does not change the result \(9 \times 4 = 4 \times 9\).
Arithmetic Operations
Arithmetic operations are the building blocks of mathematics. They include addition, subtraction, multiplication, division, and exponentiation.
They follow a hierarchical order when combined in expressions. This order is remembered using the PEMDAS rule. Understanding each operation and the order in which to apply them is critical for solving problems accurately.
Each arithmetic operation has unique properties that can simplify calculations, such as the commutative property for addition and multiplication, which allows you to swap the order of the numbers.

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

Find the average rate as indicated. The United States postal service receives 38 million changes of address per year. Find the rate per day. Round to the nearest thousand.

In any triangle, the sum of the measures of the angles is \(180^{\circ}\). In triangle \(A B C, \angle A\) is four times as large as \(\angle B\). Angle \(C\) measures \(20^{\circ}\) less than \(\angle B\). Find the measure of each angle.

Use the following information. You open a snack stand at a fair. The income and expenses (in dollars) for selling each type of food are shown in the matrices. \(\begin{array}{ccccccc}\text { Day 1 } & \text { Income } & \text { Expenses } & \text { Day 2 } & \text { Income } & \text { Expenses } \\ \text { Hamburgers } & 72 & 14 & \text { Hamburgers } & 62 & 10 \\ \text { Hot dogs } & 85 & 18 & \text { Hot dogs } & 52 & 11 \\ \text { Tacos } & 46 & 19 & \text { Tacos } & 72 & 26\end{array}\) What were your total income and expenses for selling each type of food for the two days of the fair?

Write the verbal sentence as an equation. A number divided by 6 is 32 .

Use the following information. You open a snack stand at a fair. The income and expenses (in dollars) for selling each type of food are shown in the matrices. \(\begin{array}{ccccccc}\text { Day 1 } & \text { Income } & \text { Expenses } & \text { Day 2 } & \text { Income } & \text { Expenses } \\ \text { Hamburgers } & 72 & 14 & \text { Hamburgers } & 62 & 10 \\ \text { Hot dogs } & 85 & 18 & \text { Hot dogs } & 52 & 11 \\ \text { Tacos } & 46 & 19 & \text { Tacos } & 72 & 26\end{array}\) Which type of food had the largest profit?
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

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.