Section 7.5: Properties of Exponents and Scientific Notation 6. Use properties of exponents to simplify. Write your answers using all positive exponents. \[ \begin{array}{l} x^{9} \cdot x^{3}= \\ \left(x^{10} y^{2}\right)\left(x^{3} y^{2}\right)= \\ \left(4 x^{3}\right)^{2}= \\ \left(\frac{x^{3} y^{5}}{2 x^{-4} y^{3}}\right)^{-2}= \end{array} \]

Step 1 ：\(x^{9} \cdot x^{3} = x^{9+3} = x^{12}\)

Step 2 ：\(\left(x^{10} y^{2}\right)\left(x^{3} y^{2}\right) = x^{10+3}y^{2+2} = x^{13}y^{4}\)

Step 3 ：\(\left(4 x^{3}\right)^{2} = 4^{2} \cdot (x^{3})^{2} = 16x^{6}\)

Step 4 ：\(\frac{x^{3} y^{5}}{2 x^{-4} y^{3}} = \frac{x^{3-(-4)} y^{5-3}}{2} = \frac{x^{7} y^{2}}{2}\)

Step 5 ：\(\left(\frac{x^{7} y^{2}}{2}\right)^{-2} = \left(\frac{2}{x^{7} y^{2}}\right)^{2} = 4x^{-14}y^{-4}\)

Step 6 ：\(4x^{-14}y^{-4} = 4x^{14}y^{4}\)