Matemáticas 1 · Tema 4

Monomios

Video

Ejemplo

Resuelve las siguientes operaciones con monomios:

(4x6y2)(−3x5y3a)=(4x^6y^2)(-3x^5y^3a) = −12x11y5a-12x^{11}y^5a
(−4x2y3a)2=(-4x^2y^3a)^2 = 16x4y6a216x^4y^6a^2
−15x3y3a530x8y3a=\dfrac{-15x^3y^3a^5}{30x^8y^3a} = −5a410x5\dfrac{-5a^4}{10x^5}
36x8y4b2=\sqrt{36x^8y^4b^2} = 6x4y2b6x^4y^2b
6x−2x2+3−2y2−5x+1−x2=6x-2x^2+3-2y^2-5x+1-x^2 = −3x2+x−2y2+4-3x^2+x-2y^2+4

Ejercicios

Bloque 1
(−7x4y2)(−5x6a3)=(-7x^4y^2)(-5x^6a^3)=
(3x2y4a3)2=(3x^2y^4a^3)^2=
−2x7y9a15x2ya=\dfrac{-2x^7y^9a}{15x^2ya}=
36x10y4a2=\sqrt{36x^{10}y^4a^2}=
−8x+6x−9x2−2y2−8+10−y=-8x+6x-9x^2-2y^2-8+10-y=
Bloque 2
(5x6y5)(−2x4a2)=(5x^6y^5)(-2x^4a^2)=
(−5x2y6a)2=(-5x^2y^6a)^2=
−12x3y2a720x9y2a3=\dfrac{-12x^3y^2a^7}{20x^9y^2a^3}=
25x8y12b6=\sqrt{25x^8y^{12}b^6}=
−3x+2x2−8+y2+8x+6−x2=-3x+2x^2-8+y^2+8x+6-x^2=
Bloque 3
(−6x4y3)(−2x5y2b)=(-6x^4y^3)(-2x^5y^2b)=
(−6x4y3b)3=(-6x^4y^3b)^3=
−4x5ya12y6x2a=\dfrac{-4x^5ya}{12y^6x^2a}=
−8x12y9b33=\sqrt[3]{-8x^{12}y^9b^3}=
5x−4+2x2−3x−7x2+5−y=5x-4+2x^2-3x-7x^2+5-y=
Bloque 4
(4x7y2)(−3x6y2a)=(4x^7y^2)(-3x^6y^2a)=
(−4x3y4a2)3=(-4x^3y^4a^2)^3=
20x4y6a3−50x7a6y6=\dfrac{20x^4y^6a^3}{-50x^7a^6y^6}=
−125x24y6b33=\sqrt[3]{-125x^{24}y^6b^3}=
2x−3+6x2−7x+2x2+8=2x-3+6x^2-7x+2x^2+8=
Bloque 5
(−9x3y5)(−4x2a4)=(-9x^3y^5)(-4x^2a^4)=
(2x5y3b2)3=(2x^5y^3b^2)^3=
−6x8y4a218x3y4a5=\dfrac{-6x^8y^4a^2}{18x^3y^4a^5}=
49x6y14a4=\sqrt{49x^6y^{14}a^4}=
−7x+3x−5x2+4y2−6+9−3y=-7x+3x-5x^2+4y^2-6+9-3y=
Bloque 6
(6x4y7)(−7x5y2b3)=(6x^4y^7)(-7x^5y^2b^3)=
(−3x5y2b4)3=(-3x^5y^2b^4)^3=
−15x6y3a525x2y8a=\dfrac{-15x^6y^3a^5}{25x^2y^8a}=
−64x9y15a63=\sqrt[3]{-64x^9y^{15}a^6}=
4x−5+3x2−9x+6x2+2=4x-5+3x^2-9x+6x^2+2=

Respuestas

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Bloque 1
(−7x4y2)(−5x6a3)=(-7x^4y^2)(-5x^6a^3) = 35x10y2a335x^{10}y^2a^3
(3x2y4a3)2=(3x^2y^4a^3)^2 = 9x4y8a69x^4y^8a^6
−2x7y9a15x2ya=\dfrac{-2x^7y^9a}{15x^2ya} = −2x5y815\dfrac{-2x^5y^8}{15}
36x10y4a2=\sqrt{36x^{10}y^4a^2} = 6x5y2a6x^5y^2a
−8x+6x−9x2−2y2−8+10−y=-8x+6x-9x^2-2y^2-8+10-y = −9x2−2x−2y2−y+2-9x^2-2x-2y^2-y+2
Bloque 2
(5x6y5)(−2x4a2)=(5x^6y^5)(-2x^4a^2) = −10x10y5a2-10x^{10}y^5a^2
(−5x2y6a)2=(-5x^2y^6a)^2 = 25x4y12a225x^4y^{12}a^2
−12x3y2a720x9y2a3=\dfrac{-12x^3y^2a^7}{20x^9y^2a^3} = −3a45x6\dfrac{-3a^4}{5x^6}
25x8y12b6=\sqrt{25x^8y^{12}b^6} = 5x4y6b35x^4y^6b^3
−3x+2x2−8+y2+8x+6−x2=-3x+2x^2-8+y^2+8x+6-x^2 = x2+5x+y2−2x^2+5x+y^2-2
Bloque 3
(−6x4y3)(−2x5y2b)=(-6x^4y^3)(-2x^5y^2b) = 12x9y5b12x^9y^5b
(−6x4y3b)3=(-6x^4y^3b)^3 = −216x12y9b3-216x^{12}y^9b^3
−4x5ya12y6x2a=\dfrac{-4x^5ya}{12y^6x^2a} = −x33y5\dfrac{-x^3}{3y^5}
−8x12y9b33=\sqrt[3]{-8x^{12}y^9b^3} = −2x4y3b-2x^4y^3b
5x−4+2x2−3x−7x2+5−y=5x-4+2x^2-3x-7x^2+5-y = −5x2+2x−y+1-5x^2+2x-y+1
Bloque 4
(4x7y2)(−3x6y2a)=(4x^7y^2)(-3x^6y^2a) = −12x13y4a-12x^{13}y^4a
(−4x3y4a2)3=(-4x^3y^4a^2)^3 = −64x9y12a6-64x^9y^{12}a^6
20x4y6a3−50x7a6y6=\dfrac{20x^4y^6a^3}{-50x^7a^6y^6} = −25x3a3\dfrac{-2}{5x^3a^3}
−125x24y6b33=\sqrt[3]{-125x^{24}y^6b^3} = −5x8y2b-5x^8y^2b
2x−3+6x2−7x+2x2+8=2x-3+6x^2-7x+2x^2+8 = 8x2−5x+58x^2-5x+5
Bloque 5
(−9x3y5)(−4x2a4)=(-9x^3y^5)(-4x^2a^4) = 36x5y5a436x^5y^5a^4
(2x5y3b2)3=(2x^5y^3b^2)^3 = 8x15y9b68x^{15}y^9b^6
−6x8y4a218x3y4a5=\dfrac{-6x^8y^4a^2}{18x^3y^4a^5} = −x53a3\dfrac{-x^5}{3a^3}
49x6y14a4=\sqrt{49x^6y^{14}a^4} = 7x3y7a27x^3y^7a^2
−7x+3x−5x2+4y2−6+9−3y=-7x+3x-5x^2+4y^2-6+9-3y = −5x2−4x+4y2−3y+3-5x^2-4x+4y^2-3y+3
Bloque 6
(6x4y7)(−7x5y2b3)=(6x^4y^7)(-7x^5y^2b^3) = −42x9y9b3-42x^9y^9b^3
(−3x5y2b4)3=(-3x^5y^2b^4)^3 = −27x15y6b12-27x^{15}y^6b^{12}
−15x6y3a525x2y8a=\dfrac{-15x^6y^3a^5}{25x^2y^8a} = −3x4a45y5\dfrac{-3x^4a^4}{5y^5}
−64x9y15a63=\sqrt[3]{-64x^9y^{15}a^6} = −4x3y5a2-4x^3y^5a^2
4x−5+3x2−9x+6x2+2=4x-5+3x^2-9x+6x^2+2 = 9x2−5x−39x^2-5x-3

Ejercicios extra 1

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Bloque 7
(−10x5y3)(6x4y2b)=(-10x^5y^3)(6x^4y^2b)=
(3x4y2a)3=(3x^4y^2a)^3=
−8x7y6a424x3y2a2=\dfrac{-8x^7y^6a^4}{24x^3y^2a^2}=
81x10y8a6=\sqrt{81x^{10}y^8a^6}=
−6x+7x−4x2+3y2−8+9−2y=-6x+7x-4x^2+3y^2-8+9-2y=
Bloque 8
(7x4y6)(−9x3b2)=(7x^4y^6)(-9x^3b^2)=
(−2x3y5b)3=(-2x^3y^5b)^3=
−5x6y7b815x2y4b3=\dfrac{-5x^6y^7b^8}{15x^2y^4b^3}=
49x6y12b4=\sqrt{49x^6y^{12}b^4}=
8x−3x2+5y2−7x+10−2x2−y=8x-3x^2+5y^2-7x+10-2x^2-y=
Bloque 9
(−7x3y4)(4x6y3a)=(-7x^3y^4)(4x^6y^3a)=
(−5x2y4b)2=(-5x^2y^4b)^2=
−12x8ya336x4a2y2=\dfrac{-12x^8ya^3}{36x^4a^2y^2}=
−27x9y6b33=\sqrt[3]{-27x^9y^6b^3}=
9x+3x2−5x−6x2+7+2y−3=9x+3x^2-5x-6x^2+7+2y-3=
Bloque 10
(5x5y2)(−8x4y3a)=(5x^5y^2)(-8x^4y^3a)=
(−4x3y2a4)2=(-4x^3y^2a^4)^2=
18x6y7a354x9a6y5=\dfrac{18x^6y^7a^3}{54x^9a^6y^5}=
−64x12y9b63=\sqrt[3]{-64x^{12}y^9b^6}=
3x−2+5x2−6x+4x2+7=3x-2+5x^2-6x+4x^2+7=
Bloque 11
(−8x6y2)(5x3y4a2)=(-8x^6y^2)(5x^3y^4a^2)=
(4x2y5b3)2=(4x^2y^5b^3)^2=
−10x9y5b335x4y2b7=\dfrac{-10x^9y^5b^3}{35x^4y^2b^7}=
64x12y6b8=\sqrt{64x^{12}y^6b^8}=
−9x+4x−6x2+2y2−7+11−4y=-9x+4x-6x^2+2y^2-7+11-4y=
Bloque 12
(3x8y3)(−6x2y6a)=(3x^8y^3)(-6x^2y^6a)=
(−2x4y3a2)3=(-2x^4y^3a^2)^3=
21x5y8a2−28x7y3a6=\dfrac{21x^5y^8a^2}{-28x^7y^3a^6}=
−216x6y12a93=\sqrt[3]{-216x^6y^{12}a^9}=
6x−8+4x2−2x−9x2+3=6x-8+4x^2-2x-9x^2+3=
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