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# Exponents and Polynomial Multiplication

### Positive Integral Exponents

If n is a positive integer and x is a real number, then n factors of x equals to x multiply n times, where x is the base and n is the power or the exponent.

### Example ### Exponents Property of Multiplication ### Example ### Exponents Property of Power of a Power ### Example ### Exponents Property of Power of a Product ### Example ### Exponents Property of Power of a Quotient ### Example ### Exponents Property of Division ### Example ### Zero as an Exponent ### Example ### Negative Integer Exponents ### Example ### Product of two Monomials

The product of two monomials made by regroup the coeffcients and variables, then multiplying the coefficients, and similar base by adding their exponents, if there is a variable whose similar term is not exist, then keep this variable as a factor of the product.

### Example ### Product of Monomial and Polynomial

To multiply a polynomial by a monomial, multiply each term of the polynomial by the monomial. This fundamental law is known as the distributive law.

### Example ### Product of Two Polynomials

To multiply polynomials by each other follow the procedure: 1. Arrange each polynomial in decending order. 2. Multiply each term of one polynomial by each term of the other polynomial. 3. Add like terms.

### Example ### The law of a square minus b square

The law of a square minus b square is the products of a plus b and a minus b, in which a, b are real numbers. ### Example ### Square a Binomial

The square of a binomial is the sum of the square of the first term, twice the product of the two terms, and the square of the second term. ### Example ### Special Products ### Example 