Dividing 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. The formula is: a^m / a^n = a^(m-n).

Front

What is the quotient of 12x^5 and 3x^2?

Back

The quotient is 4x^(5-2) = 4x^3.

Front

What happens to the exponent when you divide x^7 by x^3?

Back

The exponent is subtracted: x^7 / x^3 = x^(7-3) = x^4.

Front

What is the result of dividing 15a^4b^2 by 5ab?

Back

The result is 3a^(4-1)b^(2-1) = 3a^3b.

Front

If you divide 8x^3y^2 by 4xy, what do you get?

Back

You get 2x^(3-1)y^(2-1) = 2x^2y.

Front

What is the rule for dividing coefficients in monomials?

Back

Divide the coefficients as you would with regular numbers.

Front

How do you handle division when the bases are different?

Back

If the bases are different, you cannot combine them; simply write the result as a product of the two monomials.

Front

What is the result of (x^5y^3) / (xy)?

Back

The result is x^(5-1)y^(3-1) = x^4y^2.

Front

What is a common mistake when dividing monomials?

Back

A common mistake is to incorrectly add the exponents instead of subtracting them.