Dividing Monomials

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 divide monomials?

Back

Dividing monomials involves simplifying the expression by dividing the coefficients and subtracting the exponents of like bases.

Front

How do you simplify the division of two monomials with the same base?

Back

To simplify the division of two monomials with the same base, subtract the exponent of the denominator from the exponent of the numerator.

Front

What is the rule for dividing coefficients in monomials?

Back

When dividing coefficients in monomials, divide the numbers as you would in arithmetic.

Front

What is the result of dividing a variable raised to a power by itself?

Back

The result is 1, as long as the exponent is the same in both the numerator and denominator.

Front

How do you handle negative coefficients when dividing monomials?

Back

When dividing monomials with negative coefficients, the negative sign can be factored out, and the division is performed on the absolute values.

Front

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

Back

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

Front

What happens when you divide a monomial by a polynomial?

Back

You cannot simplify a monomial divided by a polynomial in the same way as monomials; instead, you may need to factor or use polynomial long division.

Front

What is the significance of zero exponent in monomials?

Back

Any non-zero base raised to the power of zero equals 1, which is important when simplifying expressions.

Front

How do you simplify \( \frac{4xy^2z^5}{8x^2y^4z^3} \)?

Back

Divide the coefficients (4/8 = 1/2) and subtract the exponents for like bases: \( \frac{z^2}{2xy^2} \).