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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.

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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.

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Most popular questions from this chapter

Evaluate the power. \(0^{6}\)

You are one mile from your home. You can walk at a speed of 4 miles per hour. The subway comes by every 15 minutes, and you heard one come by 3 minutes ago. The subway ride takes 8 minutes. Write a verbal model that relates the time it would take to walk home, your walking speed, and the distance to your home.

An appliance store sells two stereo models. The model without a CD player is \(\$ 350 .\) The model with a CD player is \(\$ 480 .\) Your summer job allows you to save \(\$ 50\) a week for 8 weeks. At the end of the summer, you have enough to buy the stereo without the CD player. How much would you have needed to save each week to buy the other model? Assign labels to your verbal model. Use \(m\) to represent the unknown value.

Evaluate the expression for the given value of the variable. \((L e s s o n \quad 1.1)\). $$\frac{24}{x} when x=3$$

Which table does not represent a function? $$ \begin{aligned} &(A)\\\ &\begin{array}{|c|c|} \hline \text { input } & {\text { Output }} \\ \hline 1 & {3} \\ \hline 2 & {3} \\ \hline 3 & {3} \\ \hline 4 & {3} \\ \hline \end{array} \end{aligned} $$ $$ \begin{aligned} &(B)\\\ &\begin{array}{|c|c|} \hline \text { input } & {\text { Output }} \\ \hline 1 & {2} \\ \hline 2 & {4} \\ \hline 3 & {6} \\ \hline 4 & {8} \\ \hline \end{array} \end{aligned} $$ $$ \begin{aligned} &\mathbf{C}\\\ &\begin{array}{|c|c|} \hline \text { Input } & {\text { Output }} \\ \hline 5 & {4} \\ \hline 6 & {4} \\ \hline 7 & {5} \\ \hline 8 & {5} \\ \hline \end{array} \end{aligned} $$ $$ \begin{aligned} &(\mathbf{D})\\\ &\begin{array}{|c|c|} \hline \text { Input } & {\text { Output }} \\ \hline 5 & {1} \\ \hline 5 & {3} \\ \hline 6 & {1} \\ \hline 6 & {3} \\ \hline \end{array} \end{aligned} $$
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