Exponent Rules

Front

What is the Product of Powers Rule?

Back

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

Front

Simplify: m ⋅ m^5 ⋅ m^6

Back

m^12

Front

What is the Power of a Power Rule?

Back

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

Front

Simplify: (3xy)^2

Back

9x^2y^2

Front

What is the Power of a Product Rule?

Back

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

Front

Simplify: 5x^3 ⋅ 2x

Back

10x^4

Front

What is the Quotient of Powers Rule?

Back

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

Front

Simplify: (5p^9q^3)(2pq^7)

Back

10p^10q^10

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: a^(-n) = 1/a^n.