Simplifying 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 exponents.

Front

How do you simplify a monomial raised to a power?

Back

To simplify a monomial raised to a power, you raise each factor in the monomial to that power and multiply the results.

Front

What is the product of powers rule?

Back

The product of powers rule states that when multiplying two expressions with the same base, you add the exponents.

Front

What is the quotient of powers rule?

Back

The quotient of powers rule states that when dividing two expressions with the same base, you subtract the exponent of the denominator from the exponent of the numerator.

Front

What is the power of a power rule?

Back

The power of a power rule states that when raising a power to another power, you multiply the exponents.

Front

Simplify the expression (2x^3)(3x^2). What is the result?

Back

The result is 6x^5.

Front

What happens to the exponents when multiplying two monomials with the same base?

Back

The exponents are added together.

Front

If you have the expression (x^4y^3)^2, how do you simplify it?

Back

You apply the power of a power rule: (x^4)^2 * (y^3)^2 = x^8y^6.

Front

What is the simplified form of (5a^2b^3)(2a^3b)?

Back

The simplified form is 10a^5b^4.

Front

What is the result of simplifying (4x^2y)(3xy^3)?

Back

The result is 12x^3y^4.