Divide 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

How do you divide monomials?

Back

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

Front

What is the result of dividing two monomials with the same base?

Back

The result is a monomial with the same base and the exponent equal to the difference of the exponents.

Front

What is the simplified form of \( \frac{a^m}{a^n} \)?

Back

The simplified form is \( a^{m-n} \).

Front

What happens to the exponent when dividing a variable with a negative exponent?

Back

When dividing a variable with a negative exponent, the negative exponent becomes positive in the denominator.

Front

What is the coefficient in the expression \( \frac{8w^{-2}}{20w^9} \)?

Back

The coefficient is \( \frac{8}{20} = \frac{2}{5} \).

Front

How do you simplify \( \frac{-28x^{-4}y^5}{4x^{-4}y^2} \)?

Back

First, divide the coefficients: \( \frac{-28}{4} = -7 \). Then, for the variables, subtract the exponents: \( y^{5-2} = y^3 \). The result is \( -7y^3 \).

Front

What is the simplified form of \( \frac{15x^2y^2}{12x^3y} \)?

Back

The simplified form is \( \frac{5y}{4x} \).

Front

How do you handle variables with different exponents when dividing?

Back

You subtract the exponent of the denominator from the exponent of the numerator for like bases.

Front

What is the result of \( \frac{y}{y^4} \)?

Back

The result is \( \frac{1}{y^3} \).