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 powers.

Front

How do you simplify a monomial?

Back

To simplify a monomial, combine like terms by adding or subtracting coefficients of the same variable raised to the same power.

Front

What is the product of powers property?

Back

The product of powers property states that when multiplying two powers with the same base, you add the exponents: a^m * a^n = a^(m+n).

Front

What is the power of a power property?

Back

The power of a power property states that when raising a power to another power, you multiply the exponents: (a^m)^n = a^(m*n).

Front

What is the power of a product property?

Back

The power of a product property states that when raising a product to a power, you distribute the exponent to each factor: (ab)^n = a^n * b^n.

Front

Simplify: 2x^3 * 4x^2

Back

8x^5

Front

Simplify: (3x^4y^5)^2

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9x^8y^{10}.

Front

Simplify: (2x^3y)^6

Back

64x^{18}y^6.

Front

What is a coefficient in a monomial?

Back

A coefficient is a numerical factor in a monomial, which multiplies the variable(s). For example, in 5x^2, 5 is the coefficient.

Front

What does it mean to combine like terms?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power.