Factors in the numerator with a negative exponents move to the denominator.

**Simplify**.

**Simplify**.

A common mistake is to multiply the base with the exponent when it is negative. For example,

Avoid this mistake . The correct solution is

Another useful property involves a rational expression raised to a negative exponent.

**Simplify**.

When simplifying expressions, it usually is best to simplify within the parentheses first and then apply the product and/or the quotient rule.

**Simplify**.

Scientific notation is an application of negative exponents. It is used to express very large or very small numbers.

An example of a power of ten might look like,

Use this to convert number expressed in scientific notation to a decimal.

Remember that we can obtain this same result by moving the decimal over six places to the right and filling in with the digit 0.

A power of ten might be negative,

Negative exponents appear when working with very small numbers.

Obtain the same result by moving the decimal over to the left 4 places.

**Express the number in scientific notation**.

Choose to place the decimal so that the first digit is between 1 and 10.

Multiplication is commutative, so when multiplying numbers in scientific notation multiply the decimal parts first. Next, multiply the powers of 10 using the product rule.

**Multiply**.

**Divide**.

**Video Examples on YouTube**: