# Algebra II : Negative Exponents

## Example Questions

### Example Question #1 : Exponents

Simplify the following expression

Explanation:

### Example Question #2 : Exponents

Simplify the following expression

Explanation:

### Example Question #3 : Exponents

Simplify the following expression

Explanation:

### Example Question #4 : Exponents

Simplify the following expression

Explanation:

### Example Question #1 : Negative Exponents

Solve for :

Explanation:

Raise both sides of the equation to the inverse power of  to cancel the exponent on the left hand side of the equation.

Subtract  from both sides:

### Example Question #6 : Negative Exponents

Represent the fraction using only positive exponents:

Explanation:

Negative exponents are the reciprocal of their positive counterpart. For example:

Therefore:

This simplifies to:

### Example Question #7 : Negative Exponents

Solve the equation for n:

Explanation:

Rewrite the right-hand-side so that each side has the same base:

Use the Property of Equality for Exponential Functions:

Solving for :

### Example Question #5 : Exponents

What is  the same as?

Explanation:

While a positive exponent says how many times to multiply by a number, a negative exponent says how many times to divide by the number.

To solve for negative exponents, just calculate the reciprocal.

### Example Question #1 : Negative Exponents

Solve:

Explanation:

To evaluate a negative exponent, convert the exponent to positive by taking the inverse.

Simplify: