# Laws of Exponents

**First Law: **If *a *is any real number and *m*, *n* are positive integers, there

**Example : **

Solve

**Solution**

**Second Law:** If *a *is any non-zero real number and *m, n* are positive integers, then

Simplify

**Third Law :** If *a* is any real number and *m, n* are positive integers, then

Solve

Evaluate

**Fourth Law :** If *a, b* are any real numbers and *m* is any positive integer then

Simplify

**Solution**

Simplify

**Fifth Law: **If *a, b* are real numbers and* m* is positive integer then

Evaluate

**Solution **

**Sixth law:** If *a* is any real number then .

Find the value of

**Example :** Simplify

Express as a power with the base 2.

Simplify and write the answers in the exponential form

Find *m *so that

Equating the exponents *m* + 10 = 9

*m* = 9 − 10 = − 1

Find the value of

Find the value of