5. Calcule o valor das expressões numéricas. a) $$ 5^{0}+(0,25)^{-2}-(0,5)^{-2}-2^{4} $$ b) $$ \left(2^{-1}-1\right)^{-1}+(-2)^{3} $$

Question

UpStudy AI · Accepted Answer

**a)**  
1. Calcular $$5^{0}$$:  
   $$
   5^{0} = 1
   $$
2. Calcular $$(0,25)^{-2}$$:  
   Note que $$0,25 = \frac{1}{4}$$, então:
   $$
   \left(\frac{1}{4}\right)^{-2} = 4^{2} = 16
   $$
3. Calcular $$(0,5)^{-2}$$:  
   Sabendo que $$0,5 = \frac{1}{2}$$, temos:
   $$
   \left(\frac{1}{2}\right)^{-2} = 2^{2} = 4
   $$
4. Calcular $$2^{4}$$:
   $$
   2^{4} = 16
   $$
5. Substituir na expressão:
   $$
   5^{0} + (0,25)^{-2} - (0,5)^{-2} - 2^{4} = 1 + 16 - 4 - 16
   $$
6. Efetuar as operações:
   $$
   1 + 16 = 17 \quad \text{e} \quad 4 + 16 = 20,
   $$
   $$
   17 - 20 = -3
   $$
   
**Resposta a)** $$ -3 $$

---

**b)**  
1. Calcular $$2^{-1}$$:
   $$
   2^{-1} = \frac{1}{2}
   $$
2. Subtrair 1:
   $$
   2^{-1} - 1 = \frac{1}{2} - 1 = -\frac{1}{2}
   $$
3. Inverter o valor:
   $$
   \left(-\frac{1}{2}\right)^{-1} = -2
   $$
4. Calcular $$(-2)^{3}$$:
   $$
   (-2)^{3} = -8
   $$
5. Somar os termos:
   $$
   \left(2^{-1} - 1\right)^{-1} + (-2)^{3} = -2 + (-8) = -10
   $$
   
**Resposta b)** $$ -10 $$
**a)** $$ -3 $$ **b)** $$ -10 $$

Calcule o valor das expressões numéricas.
a)
b)

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Pre Algebra Questions

Calcule o valor das expressões numéricas. a) b)