When raising a power to another power, multiply the exponents.

​Power Rule

Any non-zero base raised to the power of zero equals 1.

A fractional exponent represents a root. The denominator is the root, and the numerator is the power. 

When multiplying with the same base, add the exponents.

​Product Rule

When dividing with the same base, subtract the exponents.

Quotient Rule

Zero Exponent Rule

​Negative Exponent Rule

​Fractional Exponent Rule

A negative exponent means take the reciprocal and make the exponent positive.

Any base raised to the power of 1 is itself.

Exponent of 1

Review: Logarithm Rules and Properties

The following slide provide an overview of logarithm rules and properties. Please review before continuing to the next activity.

The logarithm of a quotient is the difference of the logarithms.

Quotient Rule

The logarithm of a number raised to an exponent is the exponent times the logarithm of the base.

The logarithm of 1 in any base is 0.

A logarithm answers the question: "To what power must the base b be raised to get x?"

​Definition of a Logarithm

The logarithm of a product is the sum of the logarithms.

Product Rule

Power Rule

Change of Base Formula

Logarithm of 1

To evaluate a logarithm with a different base, you can rewrite it using the change of base formula.

The logarithm of a base to itself is 1.

Logarithm of the Base