Using the Product Rule

Use the product rule to simplify each expression.

1. ⓐ $t^5\cdot t^3=t^{5+3}=t^8$
2. ⓑ ${\left(\mathrm{-3}\right)}^5\cdot \left(\mathrm{-3}\right)={\left(\mathrm{-3}\right)}^5\cdot {\left(\mathrm{-3}\right)}^1={\left(\mathrm{-3}\right)}^{5+1}={\left(\mathrm{-3}\right)}^6$
3. ⓒ $x^2\cdot x^5\cdot x^3$

At first, it may appear that we cannot simplify a product of three factors. However, using the associative property of multiplication, begin by simplifying the first two.

Notice we get the same result by adding the three exponents in one step.