Question

Simplifica la expresión por favor me ayudan

Answer 1

a)

$\sqrt[5]{-32}+\left(-1\right)^{\frac{2}{3}}$

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• $\sqrt[5]{-32}$

$=-32^{\frac{1}{5}}=\left(2^5\right)^{\frac{1}{5}}=2^{5\cdot \frac{1}{5}}=2$

• $\left(-1\right)^{\frac{2}{3}}$

$=\left(\left(-1\right)^{\frac{1}{3}}\right)^2=\left(-1\right)^2=\left(-1\right)^2$

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$=-2+1\\=-1$

b)

$\frac{-4^{\frac{1}{2}}-\sqrt[5]{-243}}{\sqrt{121}}$

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• $-4^{\frac{1}{2}}-\sqrt[5]{-243}$

$=-4^{\frac{1}{2}}-\left(-243^{\frac{1}{5}}\right)=-4^{\frac{1}{2}}+243^{\frac{1}{5}}$

• $\sqrt{121}$

$=\sqrt{11^2}=11^{2\cdot \frac{1}{2}}=11$

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$=\frac{-4^{\frac{1}{2}}+243^{\frac{1}{5}}}{11}$

• $4^{\frac{1}{2}}=\left(2^2\right)^{\frac{1}{2}}=2^{2\cdot \frac{1}{2}}=2$
• $243^{\frac{1}{5}}=\left(3^5\right)^{\frac{1}{5}}=3^{5\cdot \frac{1}{5}}=3$

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$=\frac{-2+3}{11}$

$=\frac{1}{11}$

c)

$\frac{\sqrt{100}-\sqrt[4]{16}}{\sqrt[18]{0}}$

$=\frac{\sqrt{100}-\sqrt[4]{16}}{0}$

$=\frac{10-2}{0}$

$=\frac{8}{0}$

d)

$-64^{\frac{1}{3}}\sqrt{100}\\=-\left(2^6\right)^{\frac{1}{3}}\sqrt{100}\\=-2^{6\cdot \frac{1}{3}}\sqrt{100}\\=-2^2\sqrt{100}\\=-4\cdot 10\\=-40$