Monomial Operations

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

How do you divide monomials?

Back

To divide monomials, divide the coefficients and subtract the exponents of like bases. For example, \( \frac{a^m}{a^n} = a^{m-n} \).

Front

What is the result of \( \frac{40x^{10}}{8x^4} \)?

Back

The result is \( 5x^6 \).

Front

How do you simplify the expression \( 11c^2d^2 - 20c^2d^2 \)?

Back

Combine like terms to get \( -9c^2d^2 \).

Front

What is the product of \( d^4 \) and \( d^5 \)?

Back

The product is \( d^9 \) because you add the exponents: \( 4 + 5 = 9 \).

Front

What is the product of \( -x^5 \) and \( y^3 \)?

Back

The product is \( -x^5y^3 \).

Front

How do you multiply monomials?

Back

To multiply monomials, multiply the coefficients and add the exponents of like bases. For example, \( (ax^m)(bx^n) = abx^{m+n} \).

Front

What is the result of \( (2xy) \cdot (5x^8y^3) \)?

Back

The result is \( 10x^9y^4 \).

Front

What is the degree of a monomial?

Back

The degree of a monomial is the sum of the exponents of its variables. For example, the degree of \( 3x^2y^3 \) is \( 2 + 3 = 5 \).

Front

What is the coefficient in a monomial?

Back

The coefficient is the numerical factor in a monomial. For example, in \( 7x^3 \), the coefficient is 7.