Solution: Step 1: Employ the commutative property of multiplication to rearrange the terms. 2 times 5 m2 n6 Step 2: Calculate the product of the constants 2 and 5. 10 m2 n6 Knowledge Notes: The problem at hand involves simplifying a mathematical expression that is a product of constants and variables with exponents. The process of simplification in this context means to combine like terms and constants to make the expression as concise as possible. The steps provided in the solution make use of the following mathematical principles: 1. Commutative Property of Multiplication: This property states that the order in which two numbers are multiplied does not change the product. In algebra, this property also applies to the multiplication of variables and constants. It allows us to rearrange the terms in an expression for convenience without altering the value of the expression. 2. Multiplication of Constants: Constants are numerical values that do not change. When multiplying constants, we simply calculate their product to get a single constant value. 3. Variables and Exponents: In the expression m2 n6, m and n are variables, and the numbers 2 and 6 are their respective exponents. The exponent indicates how many times the variable is multiplied by itself. In simplification, we do not alter the exponents of the variables unless we are combining like terms, which is not the case here. 4. LaTeX Formatting: The solution uses LaTeX to format mathematical expressions for clarity. LaTeX is a typesetting system that is widely used for the communication and publication of scientific documents. It allows for the presentation of mathematical and scientific expressions in a readable form. In summary, the solution to the problem involves using the commutative property to rearrange the terms for ease of multiplication and then multiplying the constants …

Simplify 2m^2*5n^6

The given problem is asking for the algebraic simplification of the expression that involves multiplication between two monomials. The expression is "2m^2*5n^6," which is made up of numeric coefficients (2 and 5) and variables with exponents (m^2 and n^6). The task is to combine the coefficients and arrange the variables in a simplified form according to the rules of algebraic multiplication.

$2 m^{2} \cdot 5 n^{6}$

Answer

Expert–verified

Solution:

Step 1:

Employ the commutative property of multiplication to rearrange the terms. $2 \times 5 m^{2} n^{6}$

Step 2:

Calculate the product of the constants $2$ and $5$. $10 m^{2} n^{6}$

Knowledge Notes:

The problem at hand involves simplifying a mathematical expression that is a product of constants and variables with exponents. The process of simplification in this context means to combine like terms and constants to make the expression as concise as possible.

The steps provided in the solution make use of the following mathematical principles:

Commutative Property of Multiplication: This property states that the order in which two numbers are multiplied does not change the product. In algebra, this property also applies to the multiplication of variables and constants. It allows us to rearrange the terms in an expression for convenience without altering the value of the expression.
Multiplication of Constants: Constants are numerical values that do not change. When multiplying constants, we simply calculate their product to get a single constant value.
Variables and Exponents: In the expression $m^{2} n^{6}$, $m$ and $n$ are variables, and the numbers $2$ and $6$ are their respective exponents. The exponent indicates how many times the variable is multiplied by itself. In simplification, we do not alter the exponents of the variables unless we are combining like terms, which is not the case here.
LaTeX Formatting: The solution uses LaTeX to format mathematical expressions for clarity. LaTeX is a typesetting system that is widely used for the communication and publication of scientific documents. It allows for the presentation of mathematical and scientific expressions in a readable form.

In summary, the solution to the problem involves using the commutative property to rearrange the terms for ease of multiplication and then multiplying the constants to simplify the expression. The variables and their exponents remain unchanged in this process.