91Ó°ÊÓ

In algebra, substitution is the process of replacing variables in an algebraic expression with their given numerical values. This helps us to simplify and evaluate the expression. Let’s follow the steps for the given problem:

1. The expression we need to evaluate is \( x y z^2 \).

2. We are given specific values: \( x = 2 \), \( y = -3 \), and \( z = -4 \).

3. We substitute these values into the expression: \( 2 \times (-3) \times (-4)^2 \).

This substitution enables us to transform a complex algebraic expression into a simpler numerical one, which we can then solve more easily.

Exponents represent repeated multiplication of a number by itself. When you see \( z^2 \), it means \( z \) multiplied by \( z \).

1. We have the expression: \( (-4)^2 \).
2. This means: \( (-4) \times (-4) \).
3. Multiply \( -4 \) by \( -4 \): This gives us 16 because multiplying two negative numbers results in a positive number.

Powers and exponents simplify repeated multiplication, showing us a more compact way to handle such computations. Always remember that \( a^m \) represents \( a \) multiplied by itself \( m \) times.

Multiplying integers can involve positive and negative numbers. Understanding the rules for multiplication will help you combine numbers correctly.

1. First, we had: \( 2 \times (-3) \).
2. Multiplying a positive number by a negative number yields a negative result: - This results in: \( 2 \times (-3) = -6 \).

Next, we need to multiply our result by 16:

3. Our new expression is: \( -6 \times 16 \).
4. Multiplying a negative number by a positive number results in a negative number: - So, \( -6 \times 16 = -96 \).

Remember these multiplication rules:

• Positive \( \times \) Positive = Positive
• Positive \( \times \) Negative = Negative
• Negative \( \times \) Negative = Positive
• Negative \( \times \) Positive = Negative

Using these rules helps us correctly solve arithmetic involving integers, making sure the sign of our result (positive or negative) is correct.