91Ó°ÊÓ

Coefficients are the numerical part of a term that multiplies the variable. In the given exercise, the monomials are \(\frac{1}{4} d^{5}\) and \(36 d^{2}\). The coefficients here are \( \frac{1}{4} \) and \(36\) respectively.
To multiply these coefficients together, you simply perform the multiplication of the fractions or whole numbers: \( \frac{1}{4} \times 36 = 9 \)
This is the first step in our multiplication process. By isolating and understanding the coefficients, we simplify the process of multiplying monomials.
Remember: Coefficients are just the numbers in front of the variables.

Exponents tell us how many times to multiply a number by itself. They are found in expressions like \(d^{5} \), where \(5\) is the exponent.
When multiplying monomials with the same base (here the base is \(d\)), you add the exponents. This rule comes from the properties of exponents.
In the given problem, we multiply \(d^{5}\times d^{2}\). By adding the exponents, we get: \(d^{5+2} = d^{7} \)
Understanding how to handle exponents is crucial for simplifying expressions and solving equations. Make sure to always add the exponents when multiplying like bases.

Variables are symbols that represent numbers in algebraic expressions. In our example, \(d\) is the variable that represents some value.
When dealing with variables, it is important to keep track of their exponents because, as shown, exponents indicate the power to which the variable is raised.
In monomials, variables with the same base are combined by adding their exponents. This helps to simplify the expressions down to a more manageable form.
The final combination of the variable \(d\) with its new exponent (in this case \(d^{7}\)) completes the process of multiplying the monomials.
Always pay attention to the base of the variable and ensure you correctly handle their exponents.