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Absolute Value Function
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Raising an Exponential Expression to a Power
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Scientific Notation
Like Radical Terms
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Working with Fractions
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Simplifying Expressions That Contain Negative Exponents
Rationalizing the Denominator
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Estimating Sums and Differences of Mixed Numbers
Algebraic Fractions
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Factoring Special Quadratic Polynomials
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Rules for Exponents
Finding Logarithms
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Variables and Expressions
Dividing Radicals
Using Proportions and Cross
Solving Equations with Radicals and Exponents
Natural Logs
The Addition Method
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Simplifying Expressions That Contain Negative Exponents

When we write an exponential expression in simplified form, we typically use only positive exponents.

Example 1

Simplify and write using only positive exponents: (3-1r4s-5t)-2

Solution

Use the Power of a Product Property. = (3-1)-2(r4)-2(s-5)-2(t)-2
Use the Power of a Power Property. = 32 · r-8 · s10 · t-2
Rewrite using only positive exponents.
Simplify.

So,

Note:

There’s more than one way to simplify the original expression.

For example, you could begin like this:

Then use the Power of a Product Property.

 

Example 2

Simplify and write using only positive exponents:

Solution

For each factor with a negative exponent, move the factor to the other side of the division bar and make its exponent positive.
Use the Multiplication Property of Exponents.
Evaluate 25.

So,

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