Respuesta :

20)

[tex]\bf ~~~~~~~~~~~~\textit{negative exponents}\\\\ a^{-n} \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^{-n} \qquad \qquad a^n\implies \cfrac{1}{a^{-n}} \\\\\\ \textit{also recall that }a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}} \\\\ -------------------------------[/tex]

[tex]\bf \cfrac{(-54)^2}{\sqrt[3]{(-54)^5}}\implies \cfrac{(-54)^2}{(-54)^{\frac{5}{3}}}\implies (-54)^2(-54)^{-\frac{5}{3}}\implies (-54)^{2-\frac{5}{3}} \\\\\\ (-54)^{\frac{6-5}{3}}\implies (-54)^{\frac{1}{3}}\implies \sqrt[3]{(-54)^1}\implies \sqrt[3]{(-54)} \\\\\\ \begin{cases} 54=2\cdot 3\cdot 3\cdot 3\\ \qquad 2\cdot 3^3 \end{cases}\implies \sqrt[3]{-1\cdot 2\cdot 3^3 }\implies 3\sqrt[3]{-2}[/tex]



22)

[tex]\bf -5\sqrt[3]{2x+3}=15\impliedby \textit{we first raise both sides by }^3 \\\\\\ (-5\sqrt[3]{2x+3})^3=(15)^3\implies (-5)^3(\sqrt[3]{2x+3})^3=3375 \\\\\\ (-125)(2x+3)=3375\implies 2x+3=\cfrac{3375}{-125}\implies 2x+3=-27 \\\\\\ 2x=-30\implies x=-\cfrac{30}{2}\implies x=-15[/tex]
The first one is,

[tex] - 3 \sqrt[3]{2} [/tex]
The second one is,

[tex]x = 12[/tex]
~~

I hope that helps you out!!

Any more questions, please feel free to ask me and I will gladly help you out!!

~Zoey

Otras preguntas