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3. Determina el valor numérico de cada uno de siguientes monomios según los valores numér asignados a cada variable. a. -ab para \( a=8 y b=-4 \) b. \( -\frac{1}{4} a b^{2} \) para \( a=\frac{1}{3} y b=-3 \) c. \( \frac{3}{2} x^{3} y \) para \( x=2 \) y \( y=\frac{1}{2} \) d. \( 2 x^{3} y^{4} z^{3} \) para \( x=-1, y=-3 \) y \( z=2 \) c. \( -\frac{1}{3} n^{6} m^{4} \) para \( n=2 \) y \( m=-1 \) f. \( 0.75 m^{2} n^{i} \) para \( m=-2 \) y \( n=-1 \) g. \( \frac{9}{8} s^{3} t^{2} \) para \( s=2 \) y \( t=\frac{1}{3} \) h. \( -\left[-\left(\frac{4}{5} m^{2} p^{\prime}\right]\right] \) para \( m=-5 y \) y 1

Ask by Marshall Ayala. in Colombia
Mar 14,2025

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a. 32 b. \(-\frac{3}{4}\) c. 6 d. \(-1296\) e. \(-\frac{64}{3}\) f. \(-3\) g. 1 h. 20

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Primero, calculemos los valores numéricos de cada monomio con las variables dadas. a. \( -ab = - (8)(-4) = 32 \) b. \( -\frac{1}{4} ab^{2} = -\frac{1}{4} \left(\frac{1}{3}\right)(-3)^{2} = -\frac{1}{4} \left(\frac{1}{3}\right)(9) = -\frac{3}{4} \) c. \( \frac{3}{2} x^{3} y = \frac{3}{2}(2)^{3} \left(\frac{1}{2}\right) = \frac{3}{2}(8) \left(\frac{1}{2}\right) = 12 \) d. \( 2 x^{3} y^{4} z^{3} = 2 (-1)^{3} (-3)^{4} (2)^{3} = 2 (-1)(81)(8) = -1624 \) e. \( -\frac{1}{3} n^{6} m^{4} = -\frac{1}{3} (2)^{6} (-1)^{4} = -\frac{1}{3} (64)(1) = -\frac{64}{3} \) f. \( 0.75 m^{2} n^{i} = 0.75 (-2)^{2} (-1)^{i} = 0.75 (4) (-1)^{i} = 3(-1)^{i} \) g. \( \frac{9}{8} s^{3} t^{2} = \frac{9}{8} (2)^{3} \left(\frac{1}{3}\right)^{2} = \frac{9}{8}(8) \left(\frac{1}{9}\right) = 1 \) h. \( -\left[-\left(\frac{4}{5} m^{2} p^{\prime}\right)\right] = -\left[-\left(\frac{4}{5} (-5)^{2}(1)\right)\right] = -\left[-\left(\frac{4}{5} (25)\right)\right] = -\left[-20\right] = 20 \) ¡Y ahí lo tienes! Las respuestas numéricas a los monomios son: a. 32, b. -\(\frac{3}{4}\), c. 12, d. -1624, e. -\(\frac{64}{3}\), f. \(3(-1)^{i}\), g. 1, h. 20.

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