Question

8 Resuelve como una sola potencia. [€ a- b. C. d. (-8) ³ - (-8)5 (-8)²-(-8)² 18. 110. 115 (150)⁰ (3+3) ². 6³ 6 = [(-3)³15 [(-3)²]3³ e. f. g. h. (-5)³(-5)4 (-5)²(-5)³ 7³. (-4)³[(-4)²15 [(-4)³]4. 7³ 5². (-4)³[(-4)61².5³ (5²)². (-4) (-4)⁹ [(-2)5]³. (6²)4 [(-2)³] 4.66​

Answer 1

Respuesta:

Explicación paso a paso:

a.

$\frac{(-8)^3\cdot (-8)^5} {(-8)^2\cdot (-8)^2} \\\\\frac{(-8^3)\cdot (-8^5)}{8^2\cdot 8^2} \\\\\frac{8^3\cdot 8^5}{8^2\cdot 8^2} \\\\\frac{8^{3+5}}{8^{2+2}} \\\\\frac{8^8}{8^4} \\\\8^{8-4}\\\\8^4$

b.

$\frac{1^8\cdot 1^{10}\cdot 1^{15}}{(150)^0} \\\\\frac{1\cdot 1\cdot 1}{1} \\\\1$

c.

$\frac{(3+3)^2\cdot 6^3}{6^4} \\\\\frac{6^2\cdot 6^3}{6^4} \\\\\frac{6^{2+3}}{6^4} \\\\\frac{6^5}{6^4} \\\\6^{5-4}\\\\6^1\\\\6$

d.

$\frac{[(-3)^3]^5}{[(-3)^2]^3} \\\\\frac{(-3)^{3\cdot 5}}{(-3)^{2\cdot 3}} \\\\\frac{(-3)^{15}}{(-3)^{6}}\\\\ (-3)^{15-6}\\\\(-3)^9\\\\-3^9$

e.

$[\frac{(-5)^3 \cdot (-5)^4}{(-5)^2\cdot (-5)^3} ]^2\\\\\left[ \frac{(-5)^{3+4}}{(-5)^{2+3}} \right]^2\\\\\left[ \frac{(-5)^7}{(-5)^5} \right]^2\\\\\left[ (-5)^{7-5} \right]^2\\\\\left[ (-5)^2 \right]^2\\\\(-5)^{2\cdot 2} \\\\(-5)^4\\\\5^4$

f.

$\frac{7^3 \cdot (-4)^3 \left[ (-4)^2 \right] ^{5} }{\left[ (-4)^3\right]^{4} \ \cdot 7^3 } \\\\\frac{(-4)^3\cdot (-4)^{2\cdot 5}}{(-4)^{3\cdot 4}} \\\\\frac{(-4)^3\cdot (-4)^{10}}{(-4)^{12}} \\\\\frac{(-4)^{3+10}}{(-4)^{12}} \\\\\frac{(-4)^{13}}{(-4)^{12}} \\\\(-4)^{13-12}\\\\(-4)^1\\\\-4$

g.

$\frac{5^2\cdot (-4)^3 \left[ (-4)^6 \right]^2 \cdot 5^3}{(5^2)^2\cdot (-4)^4(-4)^8 }\\\\\frac{5^{2+3}\cdot (-4)^3\cdot (-4)^{6\cdot 2}}{5^4\cdot (-4)^{4+8}} \\\\\frac{5^5\cdot (-4)^3\cdot (-4)^{12}}{5^4\cdot (-4)^{12}} \\\\\frac{5^5\cdot (-4)^{3+12}}{5^4\cdot (-4)^{12}} \\\\\frac{5^5\cdot (-4)^{15}}{5^4\cdot (-4)^{12}} \\\\5^{(5-4)}\cdot (-4)^{15-12}\\\\5^1\cdot (-4)^3\\\\5\cdot(-4^3)\\\\-5\cdot 4^3$

h.

$\left[ \frac{\left[ (-2)^5 \right]^3\cdot (6^2)^4 }{\left[ (-2)^3 \right]^4\cdot 6^6} \right] ^3\\\\\left[ \frac{(-2)^{5\cdot3}\cdot 6^{2\cdot4} }{ (-2)^{3\cdot4}\cdot 6^6} \right] ^3\\\\\left[ \frac{(-2)^{15}\cdot 6^8}{(-2)^{12}\cdot 6^6} \right]^3\\\\\left[ (-2)^{15-12}\cdot 6^{8-6} \right] ^3\\\\\left[ (-2)^3\cdot 6^2 \right]^3\\\\(-2)^{3\cdot3}\cdot 6^{2\cdot3}\\\\(-2)^9\cdot 6^6\\\\-2^9\cdot 6^6\\\\-2^9\cdot (2\cdot 3)^6\\\\-2^9\cdot 2^6 \cdot 3^6\\\\-2^{9+6}\cdot3^6\\\\-2^{15}\cdot 3^6$