Problem 38 - Algebra 1

Question

Evaluate the expression. $$24+m^{3} \text { when } m=5$$

Step-by-Step Solution

Answer

The expression \( 24+m^3 \) evaluates to 149 when \( m=5 \).

Step 1: Substituting the Value

In the first step, the value of variable \( m \), that is \( 5 \), is substituted into the expression. The expression then becomes \(24+ 5^3\)

Step 2: Calculating the Exponentiation

Next, calculate the value of \( 5^3 \) which equals to \( 125 \). So now the expression becomes \(24+ 125\)

Step 3: Performing the Addition

Lastly, add 24 and 125 which equals to \( 149 \). So the expression \( 24+m^3 \) evaluates to 149 when \( m = 5 \).

Key Concepts

Substitution

In algebra, substitution plays a key role in simplifying and solving expressions. When you have a variable in an expression, like \( m \) in \( 24 + m^3 \), substitution allows you to replace that variable with a given number. For example:
- If we're given that \( m = 5 \), we replace every instance of \( m \) in the expression with \( 5 \).
Think of substitution as a straightforward swap, helping you turn a complex algebraic expression into something more manageable. This step is essential before evaluating the rest of the expression.

Exponentiation

Exponentiation is the mathematical operation where a number, known as the base, is multiplied by itself a specified number of times. In this expression, \( m^3 \) means \( m \) multiplied by itself twice more (three times total).
For \( m = 5 \), we compute \( 5^3 \). This means:

• Multiply \( 5 \) by \( 5 \) to get 25.
• Then, multiply 25 by 5, resulting in 125.

Exponentiation increases the value rapidly depending on the size of the base and the power, adding depth to algebraic problems.

Addition

Addition is one of the fundamental operations in math, used to calculate the sum of numbers. Once you've completed your substitution and exponentiation tasks, you're left with an expression that's ready for addition.
In our case, the expression transforms into \( 24 + 125 \) after substitution and exponentiation.

• Start by aligning the numbers, usually by place value.
• Add 24 and 125 to get 149.

Addition combines values to reach a single sum, completing the problem-solving process and arriving at a final, simple solution.