5. Aplique as propriedades das potencias: a) 3^8 cdot 3^4= d) 10 x^5 cdot 2 x^3= b) x^2 div x= e) 20 y^2 div 10 y= e) [(b^2)^2]^3= f) (3^2)^3=

a) \( 3^{8} \cdot 3^{4} = 3^{8+4} = 3^{12} \)<br /><br />b) \( x^{2} \div x = x^{2-1} = x^{1} = x \)<br /><br />c) \( \left[\left(b^{2}\right)^{2}\right]^{3} = \left(b^{2 \cdot 2}\right)^{3} = \left(b^{4}\right)^{3} = b^{4 \cdot 3} = b^{12} \)<br /><br />d) \( 10 x^{5} \cdot 2 x^{3} = (10 \cdot 2) \cdot (x^{5+3}) = 20 x^{8} \)<br /><br />e) \( 20 y^{2} \div 10 y = \frac{20}{10} \cdot \frac{y^{2}}{y} = 2 y^{2-1} = 2 y \)<br /><br />f) \( \left(3^{2}\right)^{3} = 3^{2 \cdot 3} = 3^{6} \)