Question

1) a) (5x^4) . (3x²) = b) (x²y^5) . (x³y²) = c) (x²y) . (-5xy²) = d) (3x^5y²z) . (9x²yz²) = 2) a) (14x²) : (-7x) = b) (28x³y³) : (4x²y²) = c) (121x^5y^4) : (-11xy) = d) (125x³y³) : (5xy) = 3) a) (2x^5)³= b) (3x²y²)³ = c) (4a²b)² = d) (-5x²)³ = 4) a) √ 49y^4 = b) √ 36x^10 = c) √ 19y^8 = d) √ 81x² = 5) a) (2x+1) + (3x+2) = b) x²+5x+2x²+10x = c) 7x²+10x²+11x-3x = d) (7x+3) + (5x-10) = e) (10x+30) - (5x+10) = f) (3x+7) + (5x+2) = g) (2x²+5x) + (2x²-3x) = h) (a²+5xy) + (2a²-xy) = 6) a) x . (x+10) = b) 3xy . (4xy+10y) = c) 5x² . (x³+x²) = d) 7xy . (x+10y) = e) 2x . (5x²-3x+6) = 7) a) (15x³+10x²) : (5x) = b) (18x^5+9x³) : (9x²) = c) (125x^6+250x^4) : (25x²) = d) (28a^5+16a²) : (4a²) = Desafio 1 - Em um sítio existem 21 bichos, entre patos e cachorros. Se, no total, há 54 pés desses bichos, descubra o número de patos e o número de cachorros. Desafio 2 - Uma pessoa se encontra no degrau na metade de uma escada. Sobe 5 degraus, desce 7, volta a subir 4 e depois mais 9 para chegar ao último degrau. Quantos degraus a escada tem?

Answer 1

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1)

$\tt{a)}~\sf{5x^4\cdot3x^2=15x^6}\\\tt{b)}~\sf{x^2y^5\cdot x^3y^2=x^5y^7}\\\tt{c)}~\sf{x^2y\cdot(-5xy^2)=-5x^3y^3}\\\tt{d)}~\sf{(3x^5y^2z)\cdot(9x^2yz^2)=27x^7y^3z^3}$

2)

$\tt{a)}~\sf{14x^2\div(-7x)=-2x}\\\tt{b)}~\sf{(28x^3y^3)\div(4x^2y^2)=7xy}\\\tt{c)}~\sf{(121x^5y^4)\div(-11xy)=-11x^4y^3}\\\tt{d)}~\sf{(125x^3y^3)\div(5xy)=25x^2y^2}$

3)

$\tt{a)}~\sf{(2x^5)^3=8x^{15}}\\\tt{b)}~\sf{(3x^2y^2)^3=27x^4y^4}\\\tt{c)} ~\sf{(4a^2b)^2=16a^4b^2}\\\tt{d)}~\sf{(-5x^2)^3=-125x^6}$

4)

$\tt{a)}~\sf{\sqrt{49y^4}=7y^2}\\\tt{b)}~\sf{\sqrt{36x^{10}}=6x^5}\\\tt{c)}~\sf{\sqrt{19y^8}=\sqrt{19}y^4}\\\tt{d)}~\sf{\sqrt{81x^2}=9x}$

5)

$\tt{a)}~\sf{(2x+1)+(3x+2)=5x+3}\\\tt{b)}~\sf{x^2+5x+2x^2+10x=3x^2+15x}\\\tt{c)}~\sf{7x^2+10x^2+11x-3x=17x^2+8x}\\\tt{d)}~\sf{(7x+3)+(5x-10)=12x-7}\\\tt{e)}~\sf{(10x+30)-(5x+10)=5x+20}\\\tt{f)}~\sf{(3x+7)+(5x+2)=8x+9}\\\tt{g)}~\sf{(2x^2+5x)+(2x^2-3x)=4x^2+2x}\\\tt{h)}~\sf{(a^2+5xy)+(2a^2-xy)=3a^2+4xy}$

6)

$\tt{a)}~\sf{x\cdot(x+10)=x^2+10x}\\\tt{b)}~\sf{3xy\cdot(4xy+10y)=12x^2y^2+30xy^2}\\\tt{c)}~\sf{5x^2\cdot(x^3+x^2)=5x^5+5x^4}\\\tt{d)}~\sf{7xy\cdot(x+10y)=7x^2y+70xy^2}\\\tt{e)}~\sf{2x\cdot(5x^2-3x+6)=10x^3-6x^2+12x}$

7)

$\tt{a)}~\sf{(15x^3+10x^2)\div(5x)=3x^2+2x}\\\tt{b)}~\sf{(18x^5+9x^3)\div(9x^2)=2x^3+x}\\\tt{c)}~\sf{(125x^6+250x^4)\div(25x^2)=5x^4+10x^2}\\\tt{d)}~\sf{(28a^5+16a^2)\div(4a^2)=7a^3+4}$

Desafio 1:

$\begin{cases}\sf{p+c=21}\\\sf{2p+4c=54}\end{cases}\\+\underline{\begin{cases}\sf{-\diagdown\!\!\!\!\!\!2p-2c=-42}\\\sf{\diagdown\!\!\!\!\!2p+4c=54}\end{cases}}\\\sf{2c=12}\\\sf{c=\dfrac{12}{2}}\\\sf{c=6}\\\sf{p+c=21}\\\sf{p+6=21}\\\sf{p=21-6}\\\sf{p=15}$

$\tt{Portanto~h\acute{a}~15~patos~e~6~cachorros}$