91Ó°ÊÓ

Substitution in mathematics involves replacing variables with given numerical values. This is useful when solving expressions or equations. In our exercise, we needed to evaluate the expression \(s^t\) where specific values for \(s\) and \(t\) were provided.

• The value given for \(s\) was \(-2\).
• The value for \(t\) was \(3\).

Substitution simply means we take these values and plug them into the expression. So, \(s^t\) becomes \((-2)^3\) with the given values.When substituting, be sure to replace every instance of the variable with its corresponding value. It helps to use parentheses for clarity, especially with negative numbers or multiple terms.
Substitution is powerful because it allows us to simplify complex problems by dealing with concrete numbers instead of abstract letters.

Negative numbers can often trip students up, especially in operations involving exponents. Understanding how negative numbers behave when raised to powers is crucial.When you have a negative base, such as \(-2\), the result depends on whether the exponent is even or odd:

• If the exponent is even, the product is positive because a negative times a negative is a positive.
• If the exponent is odd, the product remains negative.

In our exercise, we calculated \((-2)^3\), which is a negative number raised to an odd power (3). Each multiplication of a negative number keeps the outcome negative, as seen in multiplying \((-2)\times(-2) = 4\) and then \(4\times(-2) = -8\).
Being careful about the signs is often what makes these calculations accurate.

The order of operations is a fundamental concept in mathematics that dictates the sequence in which operations should be carried out to consistently solve expressions accurately. The conventional rule can be remembered by the acronym PEMDAS:

• Parentheses
• Exponents
• Multiplication
• Division
• Addition
• Subtraction

In our example, after substituting values, we had \((-2)^3\). According to PEMDAS, we first handle the exponent before any other operations. So, we calculated \((-2)\times(-2)\times(-2)\) before performing any additions or subtractions, if there were any. Correctly following the order ensures that expressions are simplified and solved correctly, preventing any mishaps in math problems.