Respuesta:
En el Paso a Paso
Explicación paso a paso:
Propiedades de la Potencia:
a) [tex]a^{6} .a^{3} = a^{6+3} = a^{9}[/tex]
b) [tex]a^{-5} .a^{1} = a^{-5+1} = a^{-4}[/tex]
c) [tex]b^{1} .b^{x} = b^{1+x}[/tex]
d) [tex](p^{5} )^{6} = p^{5.6} = p^{30}[/tex]
e) [tex](b^{-2} )^{-8} = b^{-2 . -8} = b^{16}[/tex]
f) [tex](-3)^{a} .4^{a} = -3^{a}. 4^{a} = (-3.4)^{a} = (-12)^{a}[/tex]
g) [tex](\frac{1}{3} )^{x} . (\frac{6}{5} )^{x} = (\frac{1}{3} . \frac{6}{5})^{x} = (\frac{6}{15})^{x} = (\frac{2}{5} )^{x}[/tex]
h) [tex](3mn^{2})^{4} = (3)^{4} .m^{4} .n^{2.4} = 81.m^{4} .n^{8}[/tex]
i) [tex]((3x)^{2} . (5x^{3})^{2} )^{3} = (3^{2} )^{3} .(x^{2} )^{3} .(5^{2} )^{3} .((x^{3} )^{2})^{3} = (3)^{6} .x^{6} .(5)^{6} .x^{18} = 729. x^{24} .15625 = 4359375.x^{24}[/tex]
j) [tex](\frac{a^{2x} }{a^{3} } )^{3} = \frac{a^{6x} }{a^{9} } = a^{6x-9}[/tex]
k) [tex](\frac{w^{3-m} }{w^{m} } )^{-1} = \frac{w^{m-3} }{w^{-m} } = w^{m-3+m} = w^{2m-3}[/tex]
