Divide Monomials

Divide Monomials

When dividing monomials, simplify the coefficients and the variables separately.

1) Divide the numerical part

Divide the numbers in front of the variables, just as you would with ordinary fractions.

2) Subtract exponents for like bases

For each variable that appears in both monomials, divide by subtracting exponents:

• (x^a / x^b = x^{a-b})
• Do the same for other matching bases, such as (y), (a), or (m).

3) Keep variables that appear only once

If a variable appears only in the numerator, it stays there. If it appears only in the denominator, it moves to the denominator unless the problem expects a simplified positive-exponent form.

4) Simplify fully

Write the result with no common factors left. If needed, rewrite negative exponents in a more standard form.

Check your answer

Multiply your final answer by the divisor. You should get the original monomial in the numerator.

Example pattern

If the problem looks like (\frac{12x^5y^2}{3x^2y}), then:

1. Divide coefficients: (12/3=4)
2. Subtract exponents: (x^{5-2}=x^3), (y^{2-1}=y)
3. Final answer: (4x^3y)

Work carefully and keep the exponent rules consistent.