Exponent Rules

Front

What is the Quotient Rule for exponents?

Back

The Quotient Rule states that when dividing two powers with the same base, you subtract the exponents: a^m / a^n = a^(m-n).

Front

Simplify: 6^30 / 6^22

Back

6^8 (using the Quotient Rule: 30 - 22 = 8).

Front

What is the Product Rule for exponents?

Back

The Product Rule states that when multiplying two powers with the same base, you add the exponents: a^m * a^n = a^(m+n).

Front

Simplify: 6x^2 ⋅ 2y^4 ⋅ x

Back

12x^3y^4 (using the Product Rule: 6*2=12 and x^2*x=x^(2+1)=x^3).

Front

What is the Power of a Power Rule?

Back

The Power of a Power Rule states that when raising a power to another power, you multiply the exponents: (a^m)^n = a^(m*n).

Front

Simplify: (x^14)^3

Back

x^42 (using the Power of a Power Rule: 14*3=42).

Front

What are like terms?

Back

Like terms are terms that have the same variable raised to the same power. They can be combined by adding or subtracting their coefficients.

Front

Combine like terms: (5x + 2) + (4x + 5)

Back

9x + 7 (combine 5x and 4x, and 2 and 5).

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: 7^0

Back

1 (using the Zero Exponent Rule).