### Exponent Laws

You will need to know exponent laws very well for the ACT examination.

Remember that when the base numbers are the same and you need to multiply, you can add the exponents.

**Example 1:**

11^{5} × 11^{3} = ?

The base number in this example is 11.

So, we add the exponents: 5 + 3 = 8

That is:

11^{5} × 11^{3} =

11^{(5 + 3)} =

11^{8}

However, when the base numbers are the same and you need to divide, you can subtract the exponents.

**Example 2:**

10^{6} ÷ 10^{4} = ?

The base number in this example is 10.

So, we subtract the exponents: 6 − 4 = 2

That is:

10^{6} ÷ 10^{4} =

10^{(6 − 4)} =

10^{2}

Now try this practical problem, using the laws of exponents stated above.

**Example 3:**

A flight with a low-cost airline travels 9 × 10^{3} miles per hour for 3 × 10^{−2} hours.

How far has this flight traveled?

A. 135 miles

B. 270 miles

C. 900 miles

D. 1350 miles

E. 2700 miles

**The correct answer is B.**

As stated above, when the base numbers are the same and you need to multiply, you can add the exponents.

In this problem, we need to multiply the miles per hour times the number of hours in order to calculate the distance traveled.

Since we have the base number of 10 for each number that has an exponent, we can add the exponent of 3 to the exponent of −2:

(9 × 10^{3} miles per hour) × (3 × 10^{−2} hours) =

9 × 3 × 10^{(3 + −2)} =

9 × 3 × 10^{1} =

9 × 3 × 10 = 270 miles