Exponents and Polynomial Operations

Front

What is an exponent?

Back

An exponent is a number that indicates how many times to multiply the base by itself. For example, in 2^3, 2 is the base and 3 is the exponent, meaning 2 is multiplied by itself 3 times (2 * 2 * 2 = 8).

Front

What is the zero exponent rule?

Back

Any non-zero number raised to the power of 0 is equal to 1. For example, 5^0 = 1.

Front

What is the product of powers property?

Back

When multiplying two powers with the same base, you add the exponents. For example, a^m * a^n = a^(m+n).

Front

What is the power of a power property?

Back

When raising a power to another power, you multiply the exponents. For example, (a^m)^n = a^(m*n).

Front

What is the power of a product property?

Back

When raising a product to a power, you apply the exponent to each factor. For example, (ab)^n = a^n * b^n.

Front

What is the quotient of powers property?

Back

When dividing two powers with the same base, you subtract the exponents. For example, a^m / a^n = a^(m-n).

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, 3x^2 + 2x + 1 is a polynomial.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest exponent of the variable in the expression. For example, in 4x^3 + 2x^2 + 5, the degree is 3.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms. For example, (3x^2 + 2x) + (4x^2 + 5) = 7x^2 + 2x + 5.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (5x^2 + 3) - (2x^2 + 1) = 3x^2 + 2.