Operations with Monomials (multiplying & dividing exponents)

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 exponents.

Front

What does it mean to combine like terms?

Back

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power.

Front

How do you multiply monomials?

Back

To multiply monomials, multiply the coefficients and add the exponents of like bases. For example, (3x^2)(4x^3) = 12x^(2+3) = 12x^5.

Front

How do you divide monomials?

Back

To divide monomials, divide the coefficients and subtract the exponents of like bases. For example, (12x^5)/(3x^2) = 4x^(5-2) = 4x^3.

Front

What is the product of powers property?

Back

The product of powers property states that when multiplying two powers with the same base, you add the exponents: a^m * a^n = a^(m+n).

Front

What is the quotient of powers property?

Back

The quotient of powers property states that when dividing two powers with the same base, you subtract the exponents: a^m / a^n = a^(m-n).

Front

What is the zero exponent rule?

Back

The zero exponent rule states that any non-zero base raised to the power of zero equals one: a^0 = 1 (where a ≠ 0).

Front

What is the negative exponent rule?

Back

The negative exponent rule states that a negative exponent indicates the reciprocal of the base raised to the opposite positive exponent: a^(-n) = 1/(a^n) (where a ≠ 0).

Front

Simplify: 4x^3 * 2x^2

Back

8x^5.

Front

Simplify: (x^4)/(x^2)

Back

x^2.