The document you provided contains several math problems related to simplifying expressions, solving equations, and working with powers. Here's a breakdown of the questions:

2. Simplify the expressions fully, without using a calculator.

• (a) $125^{\frac{2}{3}}$
• (b) $\frac{3^{n-1} \times 9^{n+1} \times 3^n}{27^{n-1}}$
• (c) \frac{9^{2n} \times 12^{n}}}{36^{n+1}}

3. Given the expression:

$\frac{4^{x+1} + 4^{x-1}}{17^{12x}}$

• (a) Simplify the expression fully.
• (b) If $3^x = 4^x$, express $\frac{4^{x+1} + 4^{x-1}}{17^{12x}}$ in terms of $t$.

4. Solve for $x$:

• (a) $3^{x^2} = 375$
• (b) $25^{2x-1} = 5^{x-3}$
• (c) $643^{x+1} \times \left( \frac{1}{16} \right)^{3x-2} = \frac{1}{8^{2}}$
• (d) $2.3^x + 3^{x-1} = 63$

5. Simplify the following expressions without using a calculator:

• (a) $(3\sqrt{2} - 6)(2\sqrt{2} + 1)$
• (b) $\sqrt{50} (\sqrt{32} - \sqrt{18})$
• (c) \frac{3\sqrt{75} - 2\sqrt{147} + \sqrt{27}}}{\sqrt{12}}

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