# Laws of Exponents

### by Annie Arnold

## Product of a Power

When multiplying powers with the same base, add the exponents.

## Power of a Power

When multiplying powers with the same base, multiply the exponents.

## Power of a Product

The exponent outside of the parentheses goes to both powers.

## Quotient of a Power

When dividing powers of the same base, subtract the exponents.

## Power of a Quotient

When dividing powers, the exponent goes to each base separately, then divided.

## Zero Exponent

When a base is to the 0 exponent, the solution is 1.

## Negative Exponent

The base is on the wrong side of the fraction line, so you need to flip the base to the other side.

## Exponential growth & Decay

Growth: when a > 0 and b > 1

Decay: when a > 0 and b is between 0 and 1## Fractional Exponents

The use of rational numbers as exponents, The root is found in the denominator and the integer exponent is found in the numerator.