Algebra Tutorials!

 Tuesday 23rd of January

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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Properties of Exponents

Example 1

Write without using a negative exponent: (5x3)-2y4

 Solution (5x3)-2y4 Use the Power of a Product Property. = (51)-2 Â· (x3)-2 Â· y4 Use the Power of a Power Property. = 51(-2) Â· x3(-2) Â· y4 Simplify. = 5-2 Â· x -6 Â· y4 Use the definition . Write 52 as 25.

So, the result is .

Example 2

 Solution Reduce the common factor of 16. Use the property to rewrite using only positive exponents. Use the Multiplication Property (add exponents). So, the result is .

Example 3

 Solution Use to rewrite using positive exponents. Use the Power of a Quotient Property. Use the Power of a Product Property. Simplify. So, the result is .
Note:

We usually write the negative sign outside of the fraction. Thus, is written as .