List the advantages and disadvantages of a computer network. List the advantages of a Local Area Network (LAN) and its disadvantages. State the advantages of a WAN and its disadvantages.

1. $(2^{3})^{2}$

Law of exponents: $(a^{m})^{n} = a^{m \times n}$.

Substitute: $(2^{3})^{2} = 2^{3 \times 2}$.

Simplify: $2^{3 \times 2} = 2^{6}$.

$\boxed{2^{6}}$

2. $(3^{2})^{3}$

Law of exponents: $(a^{m})^{n} = a^{m \times n}$.

Substitute: $(3^{2})^{3} = 3^{2 \times 3}$.

Simplify: $3^{2 \times 3} = 3^{6}$.

$\boxed{3^{6}}$

3. $(5^{2})^{4}$

Law of exponents: $(a^{m})^{n} = a^{m \times n}$.

Substitute: $(5^{2})^{4} = 5^{2 \times 4}$.

Simplify: $5^{2 \times 4} = 5^{8}$.

$\boxed{5^{8}}$

4. $(a^{3} b)^{4}$

Law of exponents: $(a^{m} b^{n})^{p} = a^{m p} b^{n p}$.

Substitute: $(a^{3} b^{1})^{4} = a^{3 \times 4} b^{1 \times 4}$.

Simplify: $a^{3 \times 4} b^{1 \times 4} = a^{12} b^{4}$.

$\boxed{a^{12} b^{4}}$

5. $2^{3} \times 2^{4}$

Law of exponents: $a^{m} \times a^{n} = a^{m + n}$.

Substitute: $2^{3} \times 2^{4} = 2^{3 + 4}$.

Simplify: $2^{3 + 4} = 2^{7}$.

$\boxed{2^{7}}$

6. $4^{2} \times 2^{3}$

Rewrite base: $4 = 2^{2}$, so $4^{2} = (2^{2})^{2}$.

Law of exponents: $(a^{m})^{n} = a^{m \times n}$.

Substitute: $(2^{2})^{2} = 2^{2 \times 2} = 2^{4}$.

Then: $2^{4} \times 2^{3}$.

Law: $a^{m} \times a^{n} = a^{m + n}$.

Substitute: $2^{4} \times 2^{3} = 2^{4 + 3} = 2^{7}$.

$\boxed{2^{7}}$

7. $4^{3} \div 2^{4}$

Rewrite base: $4 = 2^{2}$, so $4^{3} = (2^{2})^{3}$.

Law: $(a^{m})^{n} = a^{m \times n}$.

Substitute: $(2^{2})^{3} = 2^{2 \times 3} = 2^{6}$.

Then: $2^{6} \div 2^{4}$.

Law: $a^{m} \div a^{n} = a^{m - n}$.

Substitute: $2^{6} \div 2^{4} = 2^{6 - 4} = 2^{2}$.

$\boxed{2^{2}}$

8. $256 = 2^{?}$

$2^{1} = 2$ $2^{2} = 4$ $2^{3} = 8$ $2^{4} = 16$ $2^{5} = 32$ $2^{6} = 64$ $2^{7} = 128$ $2^{8} = 256$

$\boxed{8}$