Calcula las siguientes raíces. a. $$ \sqrt[3]{-64} $$ b. $$ \sqrt[4]{1296} $$ c. $$ \sqrt[6]{-729} $$ d. $$ \sqrt[3]{-1000} $$ rarquía de las operaciones con potencias raices ercita Resuelve las siguientes expresiones. a. $$ (-5)(4)-\left\{20-(-6+4)^{2}+[81 \div(-9)] ight\} $$ b. $$ 18 \div 3^{3}-4^{2} imes 2+5^{5} \div 5^{2} $$ c. $$ \frac{\sqrt{25} \cdot \sqrt[3]{64}}{2}-7 $$

Question

Calcula las siguientes raíces. a. $$ \sqrt[3]{-64} $$ b. $$ \sqrt[4]{1296} $$ c. $$ \sqrt[6]{-729} $$ d. $$ \sqrt[3]{-1000} $$ rarquía de las operaciones con potencias raices ercita Resuelve las siguientes expresiones. a. $$ (-5)(4)-\left\{20-(-6+4)^{2}+[81 \div(-9)]ight\} $$ b. $$ 18 \div 3^{3}-4^{2} 	imes 2+5^{5} \div 5^{2} $$ c. $$ \frac{\sqrt{25} \cdot \sqrt[3]{64}}{2}-7 $$

UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$\left(-729\right)^{\frac{1}{6}}$$
- step1: Evaluate the power:
  $$729^{\frac{1}{6}}\left(\frac{\sqrt{3}}{2}+\frac{1}{2}i\right)$$
- step2: Simplify:
  $$3\left(\frac{\sqrt{3}}{2}+\frac{1}{2}i\right)$$
- step3: Calculate:
  $$\frac{3\sqrt{3}}{2}+\frac{3}{2}i$$
Calculate or simplify the expression $$ (\sqrt(25)*64^(1/3))/2-7 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(\sqrt{25}\times 64^{\frac{1}{3}}\right)}{2}-7$$
- step1: Remove the parentheses:
  $$\frac{\sqrt{25}\times 64^{\frac{1}{3}}}{2}-7$$
- step2: Simplify the root:
  $$\frac{5\times 64^{\frac{1}{3}}}{2}-7$$
- step3: Reduce the fraction:
  $$5\times 2-7$$
- step4: Multiply the numbers:
  $$10-7$$
- step5: Subtract the numbers:
  $$3$$
Calculate or simplify the expression $$ (-64)^(1/3) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(-64\right)^{\frac{1}{3}}$$
- step1: Factor the number:
  $$\left(\left(-4\right)^{3}\right)^{\frac{1}{3}}$$
- step2: Evaluate the power:
  $$-4$$
Calculate or simplify the expression $$ (-5)*(4)-{20-(-6+4)^{2}+[81/(-9)]} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(-5\right)\times 4-\left(20-\left(-6+4\right)^{2}+\left(\frac{81}{\left(-9\right)}\right)\right)$$
- step1: Remove the parentheses:
  $$\left(-5\right)\times 4-\left(20-\left(-6+4\right)^{2}+\left(\frac{81}{-9}\right)\right)$$
- step2: Add the numbers:
  $$\left(-5\right)\times 4-\left(20-\left(-2\right)^{2}+\left(\frac{81}{-9}\right)\right)$$
- step3: Remove the parentheses:
  $$-5\times 4-\left(20-\left(-2\right)^{2}+\left(\frac{81}{-9}\right)\right)$$
- step4: Divide the terms:
  $$-5\times 4-\left(20-\left(-2\right)^{2}+\left(-9\right)\right)$$
- step5: Remove the parentheses:
  $$-5\times 4-\left(20-\left(-2\right)^{2}-9\right)$$
- step6: Multiply the numbers:
  $$-20-\left(20-\left(-2\right)^{2}-9\right)$$
- step7: Subtract the numbers:
  $$-20-7$$
- step8: Subtract the numbers:
  $$-27$$
Calculate or simplify the expression $$ (-1000)^(1/3) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(-1000\right)^{\frac{1}{3}}$$
- step1: Factor the number:
  $$\left(\left(-10\right)^{3}\right)^{\frac{1}{3}}$$
- step2: Evaluate the power:
  $$-10$$
Calculate or simplify the expression $$ 1296^(1/4) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$1296^{\frac{1}{4}}$$
- step1: Factor the number:
  $$\left(6^{4}\right)^{\frac{1}{4}}$$
- step2: Evaluate the power:
  $$6$$
Calculate or simplify the expression $$ 18/(3^3)-4^2*2+5^5/(5^2) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{18}{3^{3}}-4^{2}\times 2+\frac{5^{5}}{5^{2}}$$
- step1: Multiply by $$a^{-n}:$$
  $$\frac{18}{3^{3}}-4^{2}\times 2+5^{5}\times 5^{-2}$$
- step2: Divide the terms:
  $$\frac{2}{3}-4^{2}\times 2+5^{5}\times 5^{-2}$$
- step3: Multiply the terms:
  $$\frac{2}{3}-32+5^{5}\times 5^{-2}$$
- step4: Multiply the numbers:
  $$\frac{2}{3}-32+5^{3}$$
- step5: Evaluate the power:
  $$\frac{2}{3}-32+125$$
- step6: Add the numbers:
  $$\frac{2}{3}+93$$
- step7: Reduce fractions to a common denominator:
  $$\frac{2}{3}+\frac{93\times 3}{3}$$
- step8: Transform the expression:
  $$\frac{2+93\times 3}{3}$$
- step9: Multiply the numbers:
  $$\frac{2+279}{3}$$
- step10: Add the numbers:
  $$\frac{281}{3}$$
Aquí están las soluciones a las raíces y expresiones solicitadas:

### Raíces
a. $$ \sqrt[3]{-64} = -4 $$

b. $$ \sqrt[4]{1296} = 6 $$

c. $$ \sqrt[6]{-729} = \frac{3\sqrt{3}}{2} + \frac{3}{2}i $$ (esto es un número complejo, ya que la raíz de un número negativo en una raíz par da un resultado imaginario)

d. $$ \sqrt[3]{-1000} = -10 $$

### Expresiones
a. Para la expresión $$ (-5)(4)-\left\{20-(-6+4)^{2}+[81 \div(-9)]\right\} $$:
   $$
   = -20 - \left\{20 - (-2)^{2} + [-9]\right\} = -20 - \left\{20 - 4 - 9\right\} = -20 - \left\{20 - 13\right\} = -20 - 7 = -27
   $$

b. Para la expresión $$ 18 \div 3^{3}-4^{2} \times 2+5^{5} \div 5^{2} $$:
   $$
   = 18 \div 27 - 16 + 25 = \frac{2}{3} - 16 + 25 = \frac{2}{3} + 9 = \frac{2 + 27}{3} = \frac{29}{3} \approx 9.67
   $$

c. Para la expresión $$ \frac{\sqrt{25} \cdot \sqrt[3]{64}}{2}-7 $$:
   $$
   = \frac{5 \cdot 4}{2} - 7 = \frac{20}{2} - 7 = 10 - 7 = 3
   $$

### Resumen de Resultados
- Raíces:
  - a. $$ -4 $$
  - b. $$ 6 $$
  - c. $$ \frac{3\sqrt{3}}{2} + \frac{3}{2}i $$
  - d. $$ -10 $$

- Expresiones:
  - a. $$ -27 $$
  - b. $$ \frac{29}{3} $$ o aproximadamente $$ 9.67 $$
  - c. $$ 3 $$
### Raíces a. $$ \sqrt[3]{-64} = -4 $$ b. $$ \sqrt[4]{1296} = 6 $$ c. $$ \sqrt[6]{-729} = \frac{3\sqrt{3}}{2} + \frac{3}{2}i $$ (número complejo) d. $$ \sqrt[3]{-1000} = -10 $$ ### Expresiones a. $$ (-5)(4)-\left\{20-(-6+4)^{2}+[81 \div(-9)]\right\} = -27 $$ b. $$ 18 \div 3^{3}-4^{2} \times 2+5^{5} \div 5^{2} = \frac{29}{3} $$ (aproximadamente $$ 9.67 $$) c. $$ \frac{\sqrt{25} \cdot \sqrt[3]{64}}{2}-7 = 3 $$

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