Describe the product rule for integer exponents in your own words. Then, give an example of how it works.

Answer 1

The product rule for integer exponents states that when you have a power of a product, you can distribute the exponent to each individual factor within the product. This means that you can multiply the exponents for each factor to simplify the expression.

For example, if you have the expression (2^3)(2^4), you can apply the product rule to simplify it. The rule allows you to add the exponents together, so the result becomes 2^(3+4) = 2^7.

In other words, when you have the product of two numbers with the same base raised to different integer exponents, you can simplify the expression by adding the exponents and keeping the same base.