Exponent Properties and Polynomial Operations

Front

Define the Product of Powers Property.

Back

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

Front

Simplify the expression: (2a^2b^4z)(6a^3b^2z^5)

Back

12a^5b^6z^6.

Front

What is the Quotient of Powers Property?

Back

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

Front

Simplify the expression: (2x^5y^5)^5 / x^5

Back

32x^{20}y^{25}.

Front

Define the Power of a Power Property.

Back

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

Front

Simplify the expression: (2x^4y^4)(2x^3y) / 3y^2

Back

\frac{4x^7y^3}{3}.

Front

What is the Power of a Product Property?

Back

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

Front

Simplify the expression: (3x - 5)(4x^2 - 2x - 3)

Back

12x^3 - 26x^2 + x - 15.

Front

Define the Zero Exponent Rule.

Back

Any non-zero base raised to the power of zero equals one: a^0 = 1.

Front

What is the definition of a polynomial?

Back

A polynomial is an expression consisting of variables raised to non-negative integer powers and coefficients, e.g., 4x^3 - 2x + 7.