Multiplying and Dividing Monomials

Front

What is a monomial?

Back

A monomial is a polynomial with only one term, which can be a constant, a variable, or a product of constants 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 of two monomials?

Back

To divide two monomials, divide their coefficients and subtract the exponents of like bases.

Front

What is the power of a monomial?

Back

The power of a monomial is the result of raising the monomial to an exponent, which involves raising both the coefficient and the variable to that exponent.

Front

What is the coefficient in a monomial?

Back

The coefficient is the numerical factor in a monomial, which can be a whole number, fraction, or decimal.

Front

How do you simplify the expression 25x^5 / 5x^3?

Back

Divide the coefficients (25/5 = 5) and subtract the exponents of like bases (5 - 3 = 2), resulting in 5x^2.

Front

What is the result of multiplying (3c^2)(10c^7)?

Back

Multiply the coefficients (3 * 10 = 30) and add the exponents (2 + 7 = 9), resulting in 30c^9.

Front

What is the quotient rule for exponents?

Back

The quotient rule states that when dividing like bases, you subtract the exponent of the denominator from the exponent of the numerator.

Front

What is the result of (d^4)(d^5)?

Back

Multiply the coefficients (1 * 1 = 1) and add the exponents (4 + 5 = 9), resulting in d^9.

Front

How do you multiply 6x and 6x^3?

Back

Multiply the coefficients (6 * 6 = 36) and add the exponents (1 + 3 = 4), resulting in 36x^4.