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

What is the quotient rule for exponents?

Back

The quotient rule states that when dividing two powers with the same base, you subtract the exponents: a^m / a^n = a^(m-n).

Front

How do you simplify the expression 25x^5 / 5x^3?

Back

To simplify, divide the coefficients (25/5 = 5) and subtract the exponents of x (5-3 = 2), resulting in 5x^2.

Front

What is the result of dividing 10b by 2b?

Back

The result is 5, since 10/2 = 5 and the b's cancel out.

Front

What happens to the exponents when you divide like bases?

Back

When dividing like bases, you subtract the exponent of the denominator from the exponent of the numerator.

Front

Evaluate the expression x^7 / x^2 using the quotient rule.

Back

The result is x^(7-2) = x^5.

Front

What is the simplified form of (x^4y^3) / (x^2y)?

Back

The simplified form is x^(4-2)y^(3-1) = x^2y^2.

Front

How do you handle division when the numerator is a constant and the denominator is a variable?

Back

The result will be a fraction with the constant in the numerator and the variable in the denominator, e.g., 8 / x.

Front

What is the result of 12x^3 / 4x?

Back

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

Front

If a^0 = 1, what is the value of 5^0?

Back

The value of 5^0 is 1, since any non-zero number raised to the power of zero is 1.