1. Find the value of each variable that makes the equation true. \( \begin{array}{ll}\text { A. } 2^{5} \cdot 2^{3}=2^{a} & \text { a. } \frac{5^{6}}{5^{m}}=5^{9} \\ \text { B. } \frac{7}{7}_{7^{b}}=7^{-2} & \text { b. } 2^{3} \cdot 4^{n}=2^{11} \\ \text { C. } 8^{c}=\frac{1}{64} & \text { c. }\left(7^{4}\right)^{k}=7^{-8}\end{array} \)

Simplify he following fully: \( \frac{3^{3+1}-3^{-1}}{23^{x}} \) \( \frac{3^{x} \cdot 3^{1}-3^{x} \cdot 3^{-1}}{2 \cdot 3^{x}} \frac{3^{x}\left(1-\frac{1}{3}\right)}{23^{x}} \)

15 It is given that \( t=\frac{b^{2}-4}{3-b^{2}} \). Express \( b \) in terms of \( t \)

QUESTION 12 If \( 2^{x} 5^{y}=16 \times 125 \), where \( x \) and \( y \) are positive integers, determine \( x-y \) :

Câu 03: (a) Rût gơn biểu thực \[ \left(\frac{1-x}{x^{2}+x^{3}-x^{4}}-\frac{x^{2}+x+2}{x^{5}-x^{3}-2 x^{2}-x}\right):\left(\frac{1+x^{4}}{x^{3}+x^{4}+x^{5}}-\frac{1-x+x^{2}}{x}\right) \] (b) Phân tích phân thức \( \frac{1}{(x-1)(x-2)(x-3)(x-4)} \) thành tổng các phân thức dơn giản.

\( x^{2}-(k+3) x-7=0 \) seja igual a 8