Simplify using the order of operations: a) 52 - 22 b) 42 + 13 c) 103 + 82 d) 72 + 63 e) 92 - 24 f) 23 - 22 + 21 g) 103 - 3 h) 102 + 43 - 13

$$5^2 = 25$$ $$2^2 = 4$$

$$25 - 4 = 21$$

The simplified expression is $\boxed{21}$.

*b) $4^2 + 1^3$

$$4^2 = 16$$ $$1^3 = 1$$

$$16 + 1 = 17$$

The simplified expression is $\boxed{17}$.

*c) $10^3 + 8^2$

$$10^3 = 1000$$ $$8^2 = 64$$

$$1000 + 64 = 1064$$

The simplified expression is $\boxed{1064}$.

*d) $7^2 + 6^3$

$$7^2 = 49$$ $$6^3 = 216$$

$$49 + 216 = 265$$

The simplified expression is $\boxed{265}$.

*e) $9^2 - 2^4$

$$9^2 = 81$$ $$2^4 = 16$$

$$81 - 16 = 65$$

The simplified expression is $\boxed{65}$.

*f) $2^3 - 2^2 + 2^1$

$$2^3 = 8$$ $$2^2 = 4$$ $$2^1 = 2$$

$$8 - 4 + 2 = 4 + 2 = 6$$

The simplified expression is $\boxed{6}$.

*g) $10^3 - 3$

$$1000 - 3 = 997$$

The simplified expression is $\boxed{997}$.

*h) $10^2 + 4^3 - 1^3$

$$10^2 = 100$$ $$4^3 = 64$$ $$1^3 = 1$$

$$100 + 64 - 1 = 164 - 1 = 163$$

The simplified expression is $\boxed{163}$.

2. Calculate the square roots:

*a) $\sqrt{1} + \sqrt{9}$

$$\sqrt{1} = 1$$ $$\sqrt{9} = 3$$

$$1 + 3 = 4$$

The result is $\boxed{4}$.

*b) $\sqrt{4} + \sqrt{25}$

$$\sqrt{4} = 2$$ $$\sqrt{25} = 5$$

$$2 + 5 = 7$$

The result is $\boxed{7}$.

*c) $\sqrt{25} + \sqrt{16} + \sqrt{121}$

$$\sqrt{25} = 5$$ $$\sqrt{16} = 4$$ $$\sqrt{121} = 11$$

$$5 + 4 + 11 = 9 + 11 = 20$$

The result is $\boxed{20}$.

*d) $\sqrt{16} + \sqrt{144}$

$$\sqrt{16} = 4$$ $$\sqrt{144} = 12$$

$$4 + 12 = 16$$

The result is $\boxed{16}$.

*e) $\sqrt{49} + \sqrt{36}$

$$\sqrt{49} = 7$$ $$\sqrt{36} = 6$$

$$7 + 6 = 13$$

The result is $\boxed{13}$.

*f) $\sqrt{100} + \sqrt{49}$

$$\sqrt{100} = 10$$ $$\sqrt{49} = 7$$

$$10 + 7 = 17$$

The result is $\boxed{17}$.

3. Calculate using a calculator:

*a) $\sqrt{25 - 9}$

$$\sqrt{16} = 4$$

The result is $\boxed{4}$.

*b) $\sqrt{25} - 9$

$$5 - 9 = -4$$

The result is $\boxed{-4}$.

*c) $\sqrt{36} + \sqrt{9}$

$$\sqrt{36} = 6$$ $$\sqrt{9} = 3$$

$$6 + 3 = 9$$

The result is $\boxed{9}$.

*d) $\sqrt{100 - 36}$

$$\sqrt{64} = 8$$

The result is $\boxed{8}$.

*e) $\sqrt{100} - 36$

$$10 - 36 = -26$$

The result is $\boxed{-26}$.

*f) $\sqrt{16 + 9}$

$$\sqrt{25} = 5$$

The result is $\boxed{5}$.

4. Simplify using the order of operations:

*a) $(2+3)^3$

$$5^3 = 5 \times 5 \times 5 = 125$$

The simplified expression is $\boxed{125}$.

*b) $2^3 + 3^3$

$$2^3 = 8$$ $$3^3 = 27$$

$$8 + 27 = 35$$

The simplified expression is $\boxed{35}$.

*c) $10^3 - 4^3$

$$10^3 = 1000$$ $$4^3 = 64$$

$$1000 - 64 = 936$$

The simplified expression is $\boxed{936}$.

*d) $(10-4)^3$

$$6^3 = 6 \times 6 \times 6 = 216$$

The simplified expression is $\boxed{216}$.

*e) $\sqrt[3]{216} + \sqrt[3]{125}$

$$\sqrt[3]{216} = 6 \quad (\text{since } 6 \times 6 \times 6 = 216)$$ $$\sqrt[3]{125} = 5 \quad (\text{since } 5 \times 5 \times 5 = 125)$$

$$6 + 5 = 11$$

The simplified expression is $\boxed{11}$.

*f) $\sqrt[3]{8000}$

$$\sqrt[3]{8000} = 20 \quad (\text{since } 20 \times 20 \times 20 = 8000)$$

The simplified expression is $\boxed{20}$.

*g) $\sqrt[3]{8} + \sqrt[3]{1000}$

$$\sqrt[3]{8} = 2 \quad (\text{since } 2 \times 2 \times 2 = 8)$$ $$\sqrt[3]{1000} = 10 \quad (\text{since } 10 \times 10 \times 10 = 1000)$$

$$2 + 10 = 12$$

The simplified expression is $\boxed{12}$.

*h) $\sqrt[3]{64} - \sqrt[3]{27}$

$$\sqrt[3]{64} = 4 \quad (\text{since } 4 \times 4 \times 4 = 64)$$ $$\sqrt[3]{27} = 3 \quad (\text{since } 3 \times 3 \times 3 = 27)$$

$$4 - 3 = 1$$

The simplified expression is $\boxed{1}$.

*i) $\sqrt[3]{27} - \sqrt{1}$

$$\sqrt[3]{27} = 3 \quad (\text{since } 3 \times 3 \times 3 = 27)$$ $$\sqrt{1} = 1 \quad (\text{since } 1 \times 1 = 1)$$

$$3 - 1 = 2$$

The simplified expression is $\boxed{2}$.