Exponent Rules Review

Front

What are the basic exponent rules?

Back

1. Product Rule: a^m * a^n = a^(m+n) 2. Quotient Rule: a^m / a^n = a^(m-n) 3. Power Rule: (a^m)^n = a^(m*n) 4. Zero Exponent Rule: a^0 = 1 (a ≠ 0) 5. Negative Exponent Rule: a^(-n) = 1/(a^n) (a ≠ 0)

Front

What is the Product Rule for exponents?

Back

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

Front

What is the Quotient Rule for exponents?

Back

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

Front

What is the Power Rule for exponents?

Back

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

Front

What does it mean when an exponent is zero?

Back

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

Front

What does a negative exponent indicate?

Back

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent: a^(-n) = 1/(a^n) (where a ≠ 0).

Front

Simplify: x^3 * x^2

Back

Using the Product Rule: x^3 * x^2 = x^(3+2) = x^5.

Front

Simplify: (m^4)^3

Back

Using the Power Rule: (m^4)^3 = m^(4*3) = m^12.

Front

Simplify: 5^0

Back

Using the Zero Exponent Rule: 5^0 = 1.

Front

Simplify: 2^3 / 2^1

Back

Using the Quotient Rule: 2^3 / 2^1 = 2^(3-1) = 2^2.