Monomials Rules Flashcard

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 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

What is the product of two monomials?

Back

The product of two monomials is found by multiplying their coefficients and adding 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 multiplying the exponents of the variables.

Front

How do you simplify the expression (6x^2)(-3x^5)?

Back

To simplify, multiply the coefficients (6 * -3 = -18) and add the exponents of x (2 + 5 = 7), resulting in -18x^7.

Front

What is the rule for raising a power to a power?

Back

When raising a power to a power, multiply the exponents. For example, (a^m)^n = a^(m*n).

Front

How do you simplify the expression (2x^7)^3?

Back

To simplify, raise the coefficient to the power (2^3 = 8) and multiply the exponent of x (7 * 3 = 21), resulting in 8x^21.

Front

What is the quotient rule for exponents?

Back

The quotient rule states that when dividing like bases, subtract the exponents: a^m / a^n = a^(m-n).

Front

How do you simplify the expression \frac{21m^8n^5}{27m^5n^4}?

Back

Divide the coefficients (21/27 = 7/9) and subtract the exponents of like bases: m^(8-5) = m^3 and n^(5-4) = n, resulting in \frac{7}{9}m^3n.

Front

What is the square of a monomial?

Back

The square of a monomial is found by squaring the coefficient and squaring each variable, e.g., (3x^4y^5)^2 = 9x^8y^{10}.