Properties of Exponents: Product and Power

Front

What is 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: (2x^3)(3x^2)

Back

6x^5.

Front

What is 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: (x^4)^3

Back

x^{12}.

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: (2xy)^3

Back

8x^3y^3.

Front

What is the Zero Exponent Rule?

Back

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

Front

What is the value of 5^0?

Back

1.

Front

What is the Negative Exponent Rule?

Back

A negative exponent indicates the reciprocal: a^(-n) = 1/(a^n).

Front

Simplify: 3^(-2)

Back

1/9.