Exponent Rules

Front

What is the product rule for exponents?

Back

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

Front

Simplify: 6x^2 ⋅ 2y^4 ⋅ x

Back

12x^3y^4

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: (-3x^4)^3

Back

(-3)^3x^12

Front

What is the quotient rule for exponents?

Back

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

Front

Evaluate: 6^30 / 6^22

Back

6^8

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

Simplify: (x^14)^3

Back

x^42

Front

What is the negative exponent rule?

Back

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

Front

Simplify: 2^3 ⋅ 2^2

Back

2^5.