Chapter 7: Exponents and Polynomials Properties

Negative Exponent

A nonzero number raised to a negative exponent is equal to 1 divided by that number raised to the opposite (positive) exponent.

Power of a Power Property

A power raised to another power equals that base raised to the product of the exponents.

Power of a Product Property

A product raised to a power equals the product of each factor raised to that power.

Negative Power of a Quotient Property

A quotient raised to a negative power equals the reciprocal of the quotient raised to the opposite (positive) power.

Positive Power of a Quotient Property

A quotient raised to a positive power equals the quotient of each base raised to that power.

Zero Exponent

Any nonzero number raised to the zero power is 1.

Negative Integer Exponent

If n is a positive integer, find the value of 10 to the negative nth power by starting with 1 and moving the decimal point n places to the left.

Positive Integer Exponent

If n is a positive integer, find the value of 10 to the nth power by starting with 1 and moving the decimal point n places to the right.

Product of Powers Property

The product of two powers with the same base equals that base raised to the sum of the exponents.

Quotient of Powers Property

The quotient of two nonzero powers with the same base equals the base raised to the difference of the exponents.