# Algebra II : Negative Exponents

## Example Questions

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### Example Question #1 : Negative Exponents

Simplify the following expression

Explanation:

### Example Question #1 : Understanding Exponents

Simplify the following expression

Explanation:

### Example Question #3 : Negative Exponents

Simplify the following expression

Explanation:

### Example Question #4 : Negative Exponents

Simplify the following expression

Explanation:

### Example Question #1 : Understanding 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 #8 : Negative 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 #9 : Negative Exponents

Solve:

Explanation:

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

### Example Question #10 : Negative Exponents

Simplify:

Explanation:

To simplify this expression, first make all of the negative exponents positive. That means putting them in the opposite position (if they're in the numerator, put it in the denominator and vice versa).

It should then look like:

.

Then, combine like terms. Remember, if bases are the same, add exponents!