Product Rule of Exponents

When you need to multiply expressions that share the same base, you use the product rule. Instead of doing long multiplication, you keep that base and add the exponents together.

This operation works because each exponent counts how many times the base repeats as a multiplication factor.

This rule helps track long-term financial growth. Imagine investing $1,000 in a fund that doubles your money every seven years.

If the investment remains untouched for 21 years, it doubles three times, which we write as two to the power of three.

Now, if you keep that money invested for another 14 years. Over this second stretch, your money doubles two more times, written as two to the power of two.

The investment's value is represented by $1,000 times two to the power of three times two to the power of two. The two exponential factors represent the overall growth factor.

Using the product rule, add the exponents to get two to the power of five. Multiplying this by $1,000 gives an account value of $32,000.