Multiplying and Dividing Monomials

Front

What is a monomial?

Back

A monomial is a polynomial with only one term, which can be a number, a variable, or a product of numbers and variables raised to non-negative integer powers.

Front

What is the product of two monomials?

Back

To multiply two monomials, multiply their coefficients and add their exponents for like bases.

Front

What is the quotient rule for exponents?

Back

The quotient rule states that when dividing two powers with the same base, subtract the exponent of the denominator from the exponent of the numerator.

Front

How do you simplify the expression 2(4 + 9w)?

Back

Distribute the 2 to both terms inside the parentheses: 2 * 4 + 2 * 9w = 8 + 18w.

Front

What is the result of multiplying 3x^2 by 4x^3?

Back

The result is 12x^5, obtained by multiplying the coefficients (3 * 4) and adding the exponents (2 + 3).

Front

How do you divide 12x^5 by 3x^2?

Back

Divide the coefficients (12 / 3 = 4) and subtract the exponents of like bases (5 - 2 = 3), resulting in 4x^3.

Front

What is the degree of a monomial?

Back

The degree of a monomial is the sum of the exponents of its variables.

Front

What happens when you multiply a monomial by a polynomial?

Back

You distribute the monomial to each term of the polynomial, multiplying each term by the monomial.

Front

What is the simplified form of 3(2x + 1)?

Back

The simplified form is 6x + 3, obtained by distributing 3 to both terms inside the parentheses.

Front

How do you evaluate the expression 9^5?

Back

9^5 is evaluated by multiplying 9 by itself five times, resulting in 59049.