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Product of Powers Property

Suppose \(a\) is a nonzero real number and \(x\) and \(y\) are any integers,

$${a^x} \cdot {a^y} = {a^{x + y}}$$

Description: To multiply powers that have the same base, copy the common base then add the exponents.

Some examples:

$${9^2} \cdot {9^3} = {9^{2 + 3}} = {9^5}$$

$${\left( { - 2} \right)^7} \times {\left( { - 2} \right)^4} = {\left( { - 2} \right)^{7 + 4}} = {\left( { - 2} \right)^{11}}$$

$${\left( {{1 \over 2}} \right)^3} \times {\left( {{1 \over 2}} \right)^5} = {\left( {{1 \over 2}} \right)^{3 + 5}} = {\left( {{1 \over 2}} \right)^8}$$

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Laws of Exponents
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