12/12 - Laws of Exponents

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

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

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

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

What is the Zero Exponent Rule?

Back

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

Front

What is the Negative Exponent Rule?

Back

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent: a^(-n) = 1/a^n.

Front

Simplify: a^3 * a^2

Back

a^(3+2) = a^5.

Front

Simplify: (x^4)^2

Back

x^(4*2) = x^8.

Front

Simplify: (2xy)^3

Back

2^3 * x^3 * y^3 = 8x^3y^3.

Front

Simplify: x^5 / x^2

Back

x^(5-2) = x^3.