$$ \begin{array}{ll}1 & ext { Calculate the following without the use of a calculator. Show all steps! } \ 1.1 & 18-10+4-6 \ 1.2 & -24-(-18) \ 1.3 & 8 imes(-3) \div(-6) \ 1.4 & -4^{2}+(-4)^{3} \ 1.5 & \sqrt{169}-\sqrt[3]{-0,064} \ 1.6 & \sqrt{1 \frac{9}{16}} imes 1 \frac{2}{3} \div 9,3\end{array} $$

Question

$$ \begin{array}{ll}1 & 	ext { Calculate the following without the use of a calculator. Show all steps! } \ 1.1 & 18-10+4-6 \ 1.2 & -24-(-18) \ 1.3 & 8 	imes(-3) \div(-6) \ 1.4 & -4^{2}+(-4)^{3} \ 1.5 & \sqrt{169}-\sqrt[3]{-0,064} \ 1.6 & \sqrt{1 \frac{9}{16}} 	imes 1 \frac{2}{3} \div 9,3\end{array} $$

UpStudy AI · Accepted Answer

**1.1 Calculation of $$18-10+4-6$$:**

- First, subtract:  
  $$
  18-10=8
  $$
- Then, add:  
  $$
  8+4=12
  $$
- Finally, subtract:  
  $$
  12-6=6
  $$

Thus,  
$$
18-10+4-6 = 6.
$$

**1.2 Calculation of $$-24-(-18)$$:**

- Recognize that subtracting a negative is equivalent to adding the positive:  
  $$
  -24 - (-18) = -24+18
  $$
- Compute the result:  
  $$
  -24+18=-6
  $$

Thus,  
$$
-24-(-18) = -6.
$$

**1.3 Calculation of $$8\times (-3)\div(-6)$$:**

- First, multiply:  
  $$
  8\times(-3)=-24
  $$
- Then, divide:  
  $$
  -24\div(-6)=4
  $$

Thus,  
$$
8\times (-3)\div(-6)=4.
$$

**1.4 Calculation of $$-4^2+(-4)^3$$:**

- Evaluate $$ -4^2 $$ keeping in mind that the exponent applies only to $$4$$ (not the negative sign):  
  $$
  -4^2 = -(4^2) = -16
  $$
- Evaluate $$(-4)^3$$ where the negative sign is included:  
  $$
  (-4)^3 = -4\times-4\times-4 = -64
  $$
- Add the two results:  
  $$
  -16+(-64) = -80
  $$

Thus,  
$$
-4^2+(-4)^3 = -80.
$$

**1.5 Calculation of $$\sqrt{169}-\sqrt[3]{-0,064}$$:**

- Compute the square root:  
  $$
  \sqrt{169}=13
  $$
- Compute the cube root. Note that $$0,064$$ is equivalent to $$0.064$$. Since  
  $$
  0.4^3 = 0.064,
  $$
  we have  
  $$
  \sqrt[3]{0.064}=0.4.
  $$
  Because the radicand is negative,  
  $$
  \sqrt[3]{-0.064}=-0.4.
  $$
- Subtracting a negative is the same as adding:  
  $$
  13-(-0.4)=13+0.4=13.4
  $$

Thus,  
$$
\sqrt{169}-\sqrt[3]{-0,064}=13.4.
$$

**1.6 Calculation of $$\sqrt{1 \frac{9}{16}}\times 1 \frac{2}{3}\div 9,3$$:**

- Convert the mixed numbers to improper fractions:
  - $$1 \frac{9}{16}=\frac{16+9}{16}=\frac{25}{16}$$.  
    Then,  
    $$
    \sqrt{\frac{25}{16}}=\frac{5}{4}.
    $$
  - $$1 \frac{2}{3}=\frac{3+2}{3}=\frac{5}{3}$$.
- Convert the decimal written with a comma:
  - $$9,3=9.3=\frac{93}{10}$$.
- Write the expression as a multiplication and division of fractions:
  $$
  \frac{5}{4}\times\frac{5}{3}\div\frac{93}{10}=\frac{5}{4}\times\frac{5}{3}\times\frac{10}{93}.
  $$
- Multiply the fractions:
  $$
  \frac{5\times5\times10}{4\times3\times93}=\frac{250}{1116}.
  $$
- Simplify by dividing numerator and denominator by $$2$$:
  $$
  \frac{250\div2}{1116\div2}=\frac{125}{558}.
  $$

Thus,  
$$
\sqrt{1 \frac{9}{16}}\times 1 \frac{2}{3}\div 9,3=\frac{125}{558}.
$$
1.1. $$18 - 10 + 4 - 6 = 6$$ 1.2. $$-24 - (-18) = -6$$ 1.3. $$8 \times (-3) \div (-6) = 4$$ 1.4. $$-4^2 + (-4)^3 = -80$$ 1.5. $$\sqrt{169} - \sqrt[3]{-0.064} = 13.4$$ 1.6. $$\sqrt{1 \frac{9}{16}} \times 1 \frac{2}{3} \div 9.3 = \frac{125}{558}$$

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