Question

Efetua as operações:
a) (–a⁵ ) . (2a³) =

b) (4x²) . (–2xy) =

c) 2xy . (4x² – 3y + 2) =

d) 3x . ( 5x² + 3x – 1) =

e) -2x² (5x – 1) =

f) (3x – 1) . (5x² + 2) =

g) (2x² + x + 1) . (5x – 2) =

h) (12x⁶) : (6x⁴ ) =

i) (–35a⁶b⁴ ) : (7a²b³) =

j) (4x² – 6x ) : (2x ) =

k) (12m⁴ + 8m³ - 16m² ) : ( 4m² )=

l) (2a³)⁴ =

m) (2xy⁵)³ =

n (4z²)² =

o) ( – 3y )⁴ =

p) (+ 2m⁵ )⁶ =

Answer 1

Explicação passo-a-passo:

$a) \left(-a^5\right)\left(2a^3\right)\\=-a^5\cdot \:2a^3\\=-a^{5+3}\cdot \:2\\=-a^8\cdot \:2$

$b) \left(4x^2\right)\left(-2xy\right)\\=-4x^2\cdot \:2xy\\=-4x^{2+1}\cdot \:2y\\=-4x^3\cdot \:2y\\=-8x^3y$

$c) 2xy\left(4x^2-3y+2\right)\\=2xy\cdot \:4x^2+2xy\left(-3y\right)+2xy\cdot \:2\\=2\cdot \:4x^2xy-2\cdot \:3xyy+2\cdot \:2xy\\=8x^3y-6xy^2+4xy$

$d) 3x\left(5x^2+3x-1\right)\\=3x\cdot \:5x^2+3x\cdot \:3x+3x\left(-1\right)\\=3\cdot \:5x^2x+3\cdot \:3xx-3\cdot \:1\cdot \:x\\=15x^3+9x^2-3x$

$e) -2x^2\left(5x-1\right)\\=-2x^2\cdot \:5x-\left(-2x^2\right)\cdot \:1\\=-2\cdot \:5x^2x+2\cdot \:1\cdot \:x^2\\=-10x^3+2x^2$

$f) \left(3x-1\right)\left(5x^2+2\right)\\=3x\cdot \:5x^2+3x\cdot \:2+\left(-1\right)\cdot \:5x^2+\left(-1\right)\cdot \:2\\=3\cdot \:5x^2x+3\cdot \:2x-1\cdot \:5x^2-1\cdot \:2\\=15x^3-5x^2+6x-2$

$g) \left(2x^2+x+1\right)\left(5x-2\right)\\=2x^2\cdot \:5x+2x^2\left(-2\right)+x\cdot \:5x+x\left(-2\right)+1\cdot \:5x+1\cdot \left(-2\right)\\=2\cdot \:5x^2x-2\cdot \:2x^2+5xx-2x+1\cdot \:5x-1\cdot \:2\\=10x^3+x^2+3x-2$

$h) \frac{12x^6}{6x^4}\\=\frac{2x^6}{x^4}\\=2x^{6-4}\\=2x^2$

$i) \frac{-35a^6b^4}{7a^2b^3}\\=-\frac{35a^6b^4}{7a^2b^3}\\=\frac{5b^4a^{6-2}}{b^3}\\=5a^4b^{4-3}\\=-5a^4b$

$j) \frac{4x^2-6x}{2x}\\=\frac{2x\left(2x-3\right)}{2x}\\=2x-3$

$k) \frac{12m^4+8m^3-16m^2}{4m^2}\\=\frac{4m^2\left(3m^2+2m-4\right)}{4m^2}\\=3m^2+2m-4$

$l) \left(2a^3\right)^4\\=2^4\left(a^3\right)^4\\=16\left(a^3\right)^4\\=16a^{3\cdot \:4}\\=16a^{12}$

$m) \left(2xy^5\right)^3\\=2^3x^3\left(y^5\right)^3\\=8x^3\left(y^5\right)^3\\=8x^3y^{15}$

$n) \left(4z^2\right)^2\\=4^2\left(z^2\right)^2\\=16\left(z^2\right)^2\\=16z^{2\cdot \:2}\\=16z^4$

$o) \left(-3y\right)^4\\=\left(3y\right)^4\\=3^4y^4\\=81y^4$

$p) \left(2m^5\right)^6\\=64\left(m^5\right)^6\\=64m^{5\cdot \:6}\\=64m^{30}$