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In the next example we use the power rules with negative exponents.

Example

The power rules for integral exponents

Simplify each expression. Write your answers with positive exponents only. Assume that all variables represent nonzero real numbers.

Solution

= a ^{-6}

Definition of negative exponent

= 10^{ -2}x^{ (-3)(-2)}

Power rule

Power of a product rule and power rule

Because

Simplify