Laws of Exponents - Definitions & Application

Power of 1: a¹

• Anything to the zero power equals 1.

• Keep the base the same and subtract the exponents.

• Anything to the power of 1 equals itself.

• Keep the base the same and add the exponents.

• Keep the base the same and multiply the exponents.

Power of 0: a⁰

• Anything to the zero power equals 1.

• Keep the base the same and subtract the exponents.

• Anything to the power of 1 equals itself.

• Keep the base the same and add the exponents.

• Keep the base the same and multiply the exponents.

Negative Power: a^-n

• Anything to the zero power equals 1.

• Keep the base the same and subtract the exponents.

• Take the reciprocal and make the exponent positive.

• Keep the base the same and add the exponents.

• Keep the base the same and multiply the exponents.

Power of a Product: aⁿ * a^m

• Anything to the zero power equals 1.

• Keep the base the same and subtract the exponents.

• Take the reciprocal and make the exponent positive.

• Keep the base the same and add the exponents.

• Keep the base the same and multiply the exponents.

Power of a Quotient: aⁿ / a^m

• Anything to the zero power equals 1.

• Keep the base the same and subtract the exponents.

• Take the reciprocal and make the exponent positive.

• Keep the base the same and add the exponents.

• Keep the base the same and multiply the exponents.

Power of a Power: (aⁿ)^m

• Anything to the zero power equals 1.

• Keep the base the same and subtract the exponents.

• Take the reciprocal and make the exponent positive.

• Keep the base the same and add the exponents.

• Keep the base the same and multiply the exponents.

Multiplying Exponents with DIFFERENT bases and the SAME exponent: aⁿ * bⁿ

• Keep the base the same and subtract the exponents.

• Keep the exponent the same and multiply the base.

• Take the reciprocal and make the exponent positive.

• Keep the base the same and add the exponents.

• Keep the base the same and multiply the exponents.

Simplify.

• 6x¹¹

• 8x²⁴

• 8x¹¹

• 6x²⁴

Simplify.

• 6

• 5

• 5x

• 0

Simplify.

• 2x¹⁷

• 2x²³

• 5x¹⁷

• 5x²³