Problem 62 - Intermediate Algebra

Question

Use your calculator to evaluate each numerical expression. $$ (3.14)^{3} $$

Step-by-Step Solution

Answer

3.14 cubed is approximately 30.959144.

Step 1: Understand the Expression

We need to evaluate the expression \((3.14)^3\). This means we are raising 3.14 to the power of 3. In mathematical terms, this is called 'cubing'.

Step 2: Input into Calculator

Turn on your calculator and enter the base number 3.14. Then, use the exponent or power function button (usually labeled as '^' or 'EXP') on your calculator. Type in 3 as the exponent.

Step 3: Calculate the Result

After entering the expression into your calculator as \(3.14^3\), press the 'equals' button (=) to perform the computation. The calculator will compute 3.14 raised to the power of 3.

Step 4: Record the Result

The calculator should display the result, which is approximately 30.959144. Make sure to record this number accurately.

Key Concepts

Calculator Usage

Using a calculator for evaluating expressions is convenient and timesaving. Especially when dealing with complex numbers or large exponents, a calculator becomes an invaluable tool. To start, first ensure your calculator is on. Enter the base number—here, 3.14. Next, find the exponent or power function. This button might be labeled as '^', 'EXP', or have a special symbol indicating powers. Its exact form depends on the calculator model.

• Once located, press this button after entering the base number.
• Input the exponent, in this case, 3, following the power function button.

Finally, complete the calculation by pressing the 'equals' button. The calculator then processes the expression, revealing the result. Remember, practice with your calculator helps you become efficient in interpreting various functions and symbols.

Cubing Numbers

Cubing a number involves raising it to the power of three. This means multiplying the number by itself two more times. For example, with the number 3.14:

• First, multiply 3.14 by 3.14, which equals approximately 9.8596.
• Next, multiply 9.8596 by 3.14 again, yielding the final cube value of approximately 30.959144.

This concept of cubing might seem complex initially, but it's fundamentally about repetitive multiplication of the same number.
Cubing is essential in both geometry and algebra, offering applications from volume calculations of cubes to polynomial expressions. Understanding cubing numbers enhances your skills in tackling more advanced mathematical challenges.

Mathematical Expressions

Mathematical expressions are combinations of numbers, operators, and sometimes variables, forming a calculation. In the expression
o\((3.14)^3\), 3.14 is the base, and 3 is the exponent describing the operation to perform on the base.

• In expressions involving exponents, evaluating typically means multiplying the base by itself as indicated by the exponent.
• These are vital in mathematics because they condense repetitive multiplication into concise formats.

Also called 'power expressions', they offer a way to easily represent large numbers or complex calculations. Understanding how to interpret and evaluate these expressions is crucial for both basic and advanced mathematical problem solving. Notably, mastering expressions helps communicate calculations clearly, making them essential not just in academics but in daily applications where precise computations are needed.