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:
$${9^2} \cdot {9^3} = {9^{2 + 3}} = {9^5}$$
$${\left( { - 2} \right)^7} \times {\left( { - 2} \right)^4} = {\left( { - 2} \right)^{7 + 4}} = {\left( { - 2} \right)^{11}}$$
$${\left( {{1 \over 2}} \right)^3} \times {\left( {{1 \over 2}} \right)^5} = {\left( {{1 \over 2}} \right)^{3 + 5}} = {\left( {{1 \over 2}} \right)^8}$$