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Tuesday 20th of March
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 Depdendent Variable

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 Dependent Variable

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# Properties of Exponents

Exponential notation is a shorthand way of writing repeated multiplication of the same number.

For example, 53 is a shorthand way of writing 5 Â· 5 Â· 5.

In the expression 53:

â€¢ The base, 5, is the repeated factor.

â€¢ The exponent, 3, is the number of times the base appears as a factor. An exponent is also called a power.

An exponent is not always a positive real number. Here is the definition of a negative exponent:

Using this definition, we can show that:

Example 1

Write without using a negative exponent and then simplify: 6-3

Solution

 Use the definition 6-3 Write 63 as a product. Multiply. Thus,

Note

The sign of the exponent does not indicate the sign of the number.

For example, 6-3 has a negative exponent, -3. But it simplifies to a positive number.

As another example, -32 has a positive exponent. But it simplifies to a negative number: -32= -3 Â· 3 = -9

Example 2

Write without using a negative exponent: 8wy-2.

Solution

 The exponent of y is -2. Both 8 and w have an exponent of 1. 8wy-2 = 81w1y-2 For y-2, use the definition . Simplify. So, .