\begin{tabular}{|l|l}\hline 1) \( \left(x^{2}\right)\left(x^{3}\right)= \) & 7) \( 8^{-3}= \) \\ 2) \( (3 m)\left(5 m^{2}\right)= \) & 8) \( x^{-4} y^{-3}= \) \\ 3) \( \left(7 m^{3} n^{2} x\right)\left(-6 m^{-2} x^{4}\right)= \) & 9) \( \left(x^{2}\right)^{3}= \) \\ 4) \( \frac{3^{4}}{3^{2}}= \) & 10) \( \left(\frac{x}{y}\right)^{3}= \) \\ 5) \( \frac{8 m^{4}}{2 m}= \) & 11) \( \sqrt[3]{x}= \) \\ 6) \( \frac{12 x^{3} y^{4}}{4 x^{-2} y^{2}}= \) & 12) \( \sqrt[4]{2^{3}}= \)\end{tabular}

1) The expression \( \left(x^{2}\right)\left(x^{3}\right)= x^{2+3} = x^{5} \), following the property of exponent addition. It's like combining your superhero powers; the more you have, the stronger you become! 2) For \( 8^{-3} = \frac{1}{8^3} = \frac{1}{512} \), when we have a negative exponent, it tells us to flip it to its reciprocal. Life’s all about balance, even in numbers! 3) The product \( (3 m)(5 m^{2}) = 15 m^{3} \). Just multiply the numbers and add the exponents of \( m \). Remember, teamwork makes the dream work—even in algebra! 4) The expression \( \left(7 m^{3} n^{2} x\right)\left(-6 m^{-2} x^{4}\right) = -42 m^{3-2} n^{2} x^{1+4} = -42 m^{1} n^{2} x^{5} \). Make sure to combine those powers carefully like a master chemist in the lab! 5) The calculation \( \frac{3^{4}}{3^{2}} = 3^{4-2} = 3^{2} = 9 \). With exponents, division is just subtraction in disguise—always check for opportunities to simplify! 6) For \( \frac{8 m^{4}}{2 m} = 4 m^{3} \). Divide the coefficients and subtract the exponents of \( m \). Simple math is like an epic recipe; the right ingredients make all the difference! 7) When addressing \( \frac{12 x^{3} y^{4}}{4 x^{-2} y^{2}} = 3 x^{3+2} y^{4-2} = 3 x^{5} y^{2} \), it’s about taking all the components to their tips, like orchestrating a harmony in a musical ensemble! 8) \( (x^{2})^{3} = x^{2 \cdot 3} = x^{6} \). Exponentiation can feel like raising an army; when you put those powers together, you get a whole new level of strength! 9) Lastly, \( \left(\frac{x}{y}\right)^{3} = \frac{x^{3}}{y^{3}} \). When you distribute the exponent, it’s like giving every member of the team a chance to shine in the spotlight! 10) And don't forget, \( \sqrt[3]{x} = x^{\frac{1}{3}} \). Roots are just another kind of exponent in disguise. It’s down to the roots where all the magic happens! 11) Finally, for \( \sqrt[4]{2^{3}} \), it can be rewritten as \( 2^{\frac{3}{4}} \). Embrace those fractional exponents—consider them the fancy dress-up version of regular exponents!