/*! 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 35 Evaluate the variable expression... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 35

Evaluate the variable expression when a = 3 and c = 5. $$ \left(a^{2}\right) \cdot c $$

Short Answer

Expert verified
The evaluated value of the expression is 45.

Step by step solution

01

Substitute The Variables

Replace each variable in the expression with the value provided. This gives \( (3^{2}) \cdot 5 \).
02

Solve The Exponential Part

Calculate the value of \( 3^{2} \) first due to the order of operation (BIDMAS/BODMAS). This gives \( 9 \cdot 5 \).
03

Solve The Multiplication

Calculate \( 9 \cdot 5 \) to get the final result. The answer is 45.

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.

Substitution
Substitution is the process of replacing variables in an expression with their given values. Think of variables as placeholders representing numbers, and each variable can be substituted by its assigned number.

Consider the expression \((a^{2}) \cdot c\). To evaluate it, first, identify the values given for the variables, which are \(a = 3\) and \(c = 5\). Replace \(a\) with 3 and \(c\) with 5 in the expression. This transforms the expression into \((3^{2}) \cdot 5\).

This technique helps in simplifying complex algebraic expressions and finding numerical answers quickly.
Order of Operations
The order of operations is a set of rules that dictate the correct sequence to evaluate mathematical expressions. Commonly known by the acronym BIDMAS or BODMAS, which stands for:
  • Brackets
  • Indices (or Order for exponents)
  • Division and Multiplication (from left to right)
  • Addition and Subtraction (from left to right)
In the expression \((3^{2}) \cdot 5\), you first solve the exponent \((3^{2})\) because exponents come before multiplication in the order of operations.

Always follow these rules to avoid mistakes in calculations, especially in complex expressions with multiple operations.
Exponents
Exponents denote repeated multiplication of a number by itself. In mathematical terms, when you see \(a^{2}\), it means \(a \times a\).

For example, in the expression \((3^{2})\), the exponent 2 tells you to multiply 3 by itself. Thus, you calculate \(3 \times 3\), which equals 9. This simplifies our expression to \(9 \cdot 5\).

Understanding how to calculate exponents is essential for solving expressions involving powers, making it a crucial skill in algebra.

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

Determine whether the number is prime or composite. If it is composite, list all of its factors. (Skills Review p. 761) $$50$$

The Land Ordinance of 1785 divided the Northwest Territory into squares of land called townships. Every township was divided into 36 square sections, 1 mile on each side. How many square miles were in each township? How many acres? HINT: \(1 \mathrm{mi}^{2}=640\) acres

Determine whether the number is prime or composite. If it is composite, list all of its factors. (Skills Review p. 761) $$46$$

Write the expression in exponential form.(Lesson 1.2) $$ 2 b \cdot 2 b \cdot 2 b $$

Evaluate the expression for the given value of the variable. \((L e s s o n \quad 1.1)\). $$ 25-y \text { when } y=14 $$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

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.