Definition: Multiplying variables

Multiplying variables involves combining terms that have variable factors. When multiplying variables, you multiply the coefficients (if any) together and combine the variables using the rules of exponents.

Explanation:

Multiplying Coefficients: If the terms being multiplied have coefficients (numbers in front of the variables), you multiply them together. Combining Variables: Next, you combine the variables by applying the rules of exponents. Specifically, if the variables are the same, you add their exponents. For example: \$ 2x \times 3x =( 2 × 3 ) × ( x \times x ) = (6x^2) \$

Definition: Dividing Variables

Dividing variables involves separating terms with variable factors. When dividing variables, you divide the coefficients (if any) and subtract the exponent of the divisor from the exponent of the dividend, following the rules of exponents.

Explanation:

Dividing Coefficients: If the terms have coefficients, divide the coefficient of the dividend by the coefficient of the divisor. Subtracting Exponents: Then, you combine variables by subtracting the exponent of the divisor from the exponent of the dividend. For example: \$ (6x^3)/(2x) = (6/2) \times (x^3/x) = ( 3x^(3-1) ) = (3x^2) \$.