# High School Math : How to use the product rule for exponents in pre-algebra

## Example Questions

### Example Question #1 : How To Use The Product Rule For Exponents In Pre Algebra

Simplify the following expression.

Explanation:

This expression is a product of exponents with like bases. In these situations, we should use the product rule, which states that we should add the exponents.

### Example Question #2 : How To Use The Product Rule For Exponents In Pre Algebra

Simplify  without evaluating.

Cannot be simplified

Explanation:

When multilping 2 numbers with exponents, if the bases are the same, they can be combined and the exponents add together.

### Example Question #3 : How To Use The Product Rule For Exponents In Pre Algebra

Evaluate

Explanation:

The quotient rule for exponents states that when like numbers are raised to a certain power, then their exponents are subtracted from one another.

Solve for the exponent equation.

Combine like terms.

Therefore,

### Example Question #1 : How To Use The Product Rule For Exponents In Pre Algebra

Simplify the expression.

Explanation:

Since all terms are being multiplied, we can simplify by grouping like terms together.

To simplify the variable, we can add the exponents according to exponential identities.

### Example Question #5 : How To Use The Product Rule For Exponents In Pre Algebra

Simplify the expression.

Explanation:

Begin by distributing the exponent into the parentheses. Remember that each term in the parentheses must be squared.

All terms are now being multiplied. To make it simpler, we can re-group by like terms.

Multiplying exponential terms with the same base allows us to add the exponents.

### Example Question #3 : How To Use The Product Rule For Exponents In Pre Algebra

Which of the following is a simplified expression of X3X2?

Explanation:

When you multiply two exponential expressions with the same base, add the exponents to simplify the expression.

### Example Question #4 : How To Use The Product Rule For Exponents In Pre Algebra

Which of the following is an alternate expression of X3Y3?

Explanation:

When you are required to multiply exponential expressions with different bases but the same exponent, you can simplify the expression by adding parentheses and only using the exponent one time.

### Example Question #5 : How To Use The Product Rule For Exponents In Pre Algebra

Which of the following is equivalent to the expression:

?

Explanation:

Recall that when we are multiplying exponential expressions with the same base, we add the exponents and keep the base the same. Additionally, remember that adding a negative number is equivalent to subtracting.

### Example Question #6 : How To Use The Product Rule For Exponents In Pre Algebra

Simplify

Explanation:

When multiplying the same variable raised to different powers, add the powers of each term together. In this case, add  and  together to find the power of the answer, .

### Example Question #10 : How To Use The Product Rule For Exponents In Pre Algebra

Simplify the exponential expression.