91Ó°ÊÓ

Algebraic expressions are combinations of letters, numbers, and arithmetic operations such as addition, subtraction, multiplication, and division. They often use variables to represent numbers. In our original exercise, the expression involves the variable \( y \) and constants like the number 5. An example of an algebraic expression is \((5y)^{4}\), where \( y \) can take on different values.Understanding these expressions is crucial because they allow us to generalize mathematical ideas and solve problems by manipulating the expressions according to algebraic rules. Here, the letter \( y \) stands for an unknown value that is defined or can be substituted. This flexibility makes algebra a powerful tool for modeling real-world situations and solving equations.

The substitution method involves replacing a variable in an expression with its actual number value. This is helpful when we want to evaluate expressions for specific variable values. In the problem, we are asked to evaluate \((5y)^{4}\) when \( y = 2 \).To use substitution in this context:

• Identify the variable to substitute, here it is \( y \).
• Replace \( y \) with the given value, 2, to change the expression to \((5 \times 2)^{4}\).

Substitution simplifies the work by allowing a direct computation once variables are replaced with numbers. Substitution is also useful in solving systems of equations and tackling more complex algebraic problems.

Simplifying expressions entails reducing them to a more manageable form, which may involve performing operations like adding, subtracting, multiplying, and dividing numbers, or resolving powers and roots.In the exercise, after substitution, our expression becomes \((5 \cdot 2)^{4}\). The next logical step is simplification, which focuses first on the operations inside the parentheses: \(5 \cdot 2 = 10\). So our expression now is \(10^4\). The final step is to evaluate \(10^4\), which is an exponentiation. This means multiplying the base 10 by itself four times: \(10 \times 10 \times 10 \times 10\). Doing this calculation results in 10,000.Simplifying helps in making complex expressions clearer and easier to evaluate or manipulate, leading to accurate computations and problem-solving. It reduces potential errors and is an essential skill in algebra.