Ejercicio 1: $$ 3^{2}+5 \times 21-256 \div 16-35 $$ Rpta. 63 Ejercicio 4: $$ \frac{2}{9}+\frac{3}{8}-\frac{7}{4} \times \frac{1}{3}+\frac{7}{4} \div \frac{3}{4} $$ Rpta. prendido Ejercicio 2: $$ 16 \div 4+\left(5^{2}-32 \div 4\right)-(36-21) $$ Rpta. 6

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UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$3^{2}+5\times 21-\frac{256}{16}-35$$
- step1: Divide the terms:
  $$3^{2}+5\times 21-16-35$$
- step2: Multiply the numbers:
  $$3^{2}+105-16-35$$
- step3: Evaluate the power:
  $$9+105-16-35$$
- step4: Calculate:
  $$63$$
Calculate or simplify the expression $$ 16/4+(5^2-32/4)-(36-21) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{16}{4}+\left(5^{2}-\frac{32}{4}\right)-\left(36-21\right)$$
- step1: Divide the terms:
  $$\frac{16}{4}+\left(5^{2}-8\right)-\left(36-21\right)$$
- step2: Subtract the numbers:
  $$\frac{16}{4}+17-\left(36-21\right)$$
- step3: Subtract the numbers:
  $$\frac{16}{4}+17-15$$
- step4: Divide the terms:
  $$4+17-15$$
- step5: Calculate:
  $$6$$
Calculate or simplify the expression $$ 2/9+3/8-7/4*1/3+7/4/3/4 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{2}{9}+\frac{3}{8}-\frac{\frac{7}{4}\times 1}{3}+\frac{\frac{\frac{7}{4}}{3}}{4}$$
- step1: Multiply:
  $$\frac{2}{9}+\frac{3}{8}-\frac{\frac{7}{4}}{3}+\frac{\frac{\frac{7}{4}}{3}}{4}$$
- step2: Divide the terms:
  $$\frac{2}{9}+\frac{3}{8}-\frac{\frac{7}{4}}{3}+\frac{\frac{7}{12}}{4}$$
- step3: Divide the terms:
  $$\frac{2}{9}+\frac{3}{8}-\frac{7}{12}+\frac{\frac{7}{12}}{4}$$
- step4: Divide the terms:
  $$\frac{2}{9}+\frac{3}{8}-\frac{7}{12}+\frac{7}{48}$$
- step5: Reduce fractions to a common denominator:
  $$\frac{2\times 8\times 2}{9\times 8\times 2}+\frac{3\times 9\times 2}{8\times 9\times 2}-\frac{7\times 6\times 2}{12\times 6\times 2}+\frac{7\times 3}{48\times 3}$$
- step6: Multiply the terms:
  $$\frac{2\times 8\times 2}{144}+\frac{3\times 9\times 2}{8\times 9\times 2}-\frac{7\times 6\times 2}{12\times 6\times 2}+\frac{7\times 3}{48\times 3}$$
- step7: Multiply the terms:
  $$\frac{2\times 8\times 2}{144}+\frac{3\times 9\times 2}{144}-\frac{7\times 6\times 2}{12\times 6\times 2}+\frac{7\times 3}{48\times 3}$$
- step8: Multiply the terms:
  $$\frac{2\times 8\times 2}{144}+\frac{3\times 9\times 2}{144}-\frac{7\times 6\times 2}{144}+\frac{7\times 3}{48\times 3}$$
- step9: Multiply the numbers:
  $$\frac{2\times 8\times 2}{144}+\frac{3\times 9\times 2}{144}-\frac{7\times 6\times 2}{144}+\frac{7\times 3}{144}$$
- step10: Transform the expression:
  $$\frac{2\times 8\times 2+3\times 9\times 2-7\times 6\times 2+7\times 3}{144}$$
- step11: Multiply the terms:
  $$\frac{32+3\times 9\times 2-7\times 6\times 2+7\times 3}{144}$$
- step12: Multiply the terms:
  $$\frac{32+54-7\times 6\times 2+7\times 3}{144}$$
- step13: Multiply the terms:
  $$\frac{32+54-84+7\times 3}{144}$$
- step14: Multiply the numbers:
  $$\frac{32+54-84+21}{144}$$
- step15: Calculate:
  $$\frac{23}{144}$$
Aquí están las soluciones a los ejercicios:

**Ejercicio 1:**
$$
3^{2}+5 \times 21-256 \div 16-35
$$
Calculando paso a paso:
1. $$3^2 = 9$$
2. $$5 \times 21 = 105$$
3. $$256 \div 16 = 16$$

Ahora, sumamos y restamos:
$$
9 + 105 - 16 - 35 = 63
$$
**Rpta. 63**

---

**Ejercicio 4:**
$$
\frac{2}{9}+\frac{3}{8}-\frac{7}{4} \times \frac{1}{3}+\frac{7}{4} \div \frac{3}{4}
$$
Calculando paso a paso:
1. $$\frac{7}{4} \times \frac{1}{3} = \frac{7}{12}$$
2. $$\frac{7}{4} \div \frac{3}{4} = \frac{7}{3}$$

Ahora, sumamos y restamos:
$$
\frac{2}{9} + \frac{3}{8} - \frac{7}{12} + \frac{7}{3}
$$

Para sumar y restar fracciones, necesitamos un común denominador. El mínimo común múltiplo de $$9, 8, 12, 3$$ es $$72$$.

Convirtiendo cada fracción:
- $$\frac{2}{9} = \frac{16}{72}$$
- $$\frac{3}{8} = \frac{27}{72}$$
- $$\frac{7}{12} = \frac{42}{72}$$
- $$\frac{7}{3} = \frac{168}{72}$$

Ahora sumamos y restamos:
$$
\frac{16}{72} + \frac{27}{72} - \frac{42}{72} + \frac{168}{72} = \frac{169}{72}
$$

La respuesta en forma decimal es aproximadamente $$2.3472$$.

**Rpta. $$\frac{169}{72}$$ o aproximadamente $$2.3472$$**

---

**Ejercicio 2:**
$$
16 \div 4+\left(5^{2}-32 \div 4\right)-(36-21)
$$
Calculando paso a paso:
1. $$16 \div 4 = 4$$
2. $$5^2 = 25$$
3. $$32 \div 4 = 8$$
4. $$36 - 21 = 15$$

Ahora, sumamos y restamos:
$$
4 + (25 - 8) - 15 = 4 + 17 - 15 = 6
$$
**Rpta. 6**
**Ejercicio 1:** $$ 3^{2}+5 \times 21-256 \div 16-35 = 63 $$ **Ejercicio 4:** $$ \frac{2}{9}+\frac{3}{8}-\frac{7}{4} \times \frac{1}{3}+\frac{7}{4} \div \frac{3}{4} = \frac{169}{72} \text{ o } 2.3472 $$ **Ejercicio 2:** $$ 16 \div 4+\left(5^{2}-32 \div 4\right)-(36-21) = 6 $$

Ejercicio 1:

Rpta. 63
Ejercicio 4:

Rpta.
prendido

Ejercicio 2:

Rpta. 6

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Ejercicio 1: Rpta. 63 Ejercicio 4: Rpta. prendido Ejercicio 2: Rpta. 6