# Laws of Exponents

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

Example :

Example

Solve

Solution

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

Example

Simplify

Solution

Example

Solution

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

Example

Solve

Solution

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Evaluate

Solution

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

Example

Simplify

Solution

Example

Simplify

Solution

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

Example

Evaluate

Solution

Sixth law: If a is any real number then .

Example

Find the value of

Solution

Example : Simplify

Example

Express as a power with the base 2.

Solution

Example

Simplify and write the answers in the exponential form

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Find m so that

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Equating the exponents m + 10 = 9

m = 9 10 = 1

Example

Find the value of

Solution

Example

Find the value of

Solution