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

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

Simplify: 6x^2 ⋅ 2y^4 ⋅ x

Back

12x^3y^4

Front

Evaluate using the quotient rule: 6^30 / 6^8

Back

6^22

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: (2x^3y^2)^2

Back

4x^6y^4

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 happens when the base is negative and raised to an even exponent?

Back

The result is positive: (-a)^n = a^n if n is even.

Front

What happens when the base is negative and raised to an odd exponent?

Back

The result is negative: (-a)^n = -a^n if n is odd.

Front

Simplify: x^5 / x^2

Back

x^3