Question

simplifica las siguiente expresiones empleando las propiedades de la potenciación

1) (2³×3⁴×5²)³

2) 3¹²×7⁴/ 7²×3⁹

3) (3×5⁶×11⁵/ 5⁴×11⁰×(-2) )²

4) (1/3)⁷×(1/3)⁸/ (1/3)¹¹
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Answer 1

Explicación paso a paso:

1.

(2³×3⁴×5²)³=$2^{3+3} .3^{4+3} .5^{2+3} =2^{6} .3^{7}.5^{5}$

2.

3¹²×7⁴/ 7²×3⁹=$\frac{3^{12}.7^{4} }{7^{2}.3^{9} } =3^{12-9} .7^{4-2} =3^{3} .7^{2} =27.49=1323$

3.

(3×5⁶×11⁵/ 5⁴×11⁰×(-2) )²=$\frac{3^{2}.5^{6+2}.11^{5+2} }{5^{4}.1.4 } =\frac{3^{2}.5^{8}.11^{7}}{5^{4}.4 } =3^{2} .5^{8-4}.11^{7} .4^{-1} =3^{2} .5^{4}.11^{7} .4^{-1}$

4.

(1/3)⁷×(1/3)⁸/ (1/3)¹¹=$\frac{1}{3^{7} } x\frac{1}{3^{8} } =\frac{1}{3^{15} } /\frac{1}{3^{11} } =\frac{1}{3^{15} }x\frac{3^{11} }{1} =3^{11-15} =3^{-4} =(1/3)^{4} =1/81$

Suerte :v .