\[ x-3 \] 20x-10 \( x-3 \) \( 5 a-15 b \) \( 10 x^{2}(2-1) \) \( 9 a-18 a^{2} \) \( 9 a(1-2 a) \) \( 10(2 x-1) \)

140. Determina il valore di \( h \) affinché il punto \( A(4 h-2 ; 1+h) \) appartenga alla retta di equazion \( x-3 y+2=0 \). 141 Trova il valore di \( k \) affinché lo

\[ \text { Fiche: Puissances } \] Tous ces exercices sont extraits de sujets de brevet Exercice 1: Effectuer le calcul suivant et donner le résultat sous forme de fraction irréductible \[ C=\left(\frac{5}{7}\right)^{2}-\frac{2}{7} \]

A certain quadratic pattern has the following characteristics: - \( T_{1}=p \) - \( T_{2}=18 \) - \( T_{4}=4 T_{1} \) - \( T_{3}-T_{2}=10 \) Determine the value of \( p \).

(a) 3 (b) -3 2. If \( (3-x, x-1) \) lies in the fourth quadrant where \( x \in \mathbb{Z} \), then \( x= \) \( \begin{array}{ll}\text { (a) } 4 & \text { (b) } 3\end{array} \) (c) -1 (Aswan 24) (d) 1 (a) 4 (b) 3 3 If \( (125, \sqrt{y})=\left(x^{3}, 4\right) \), then \( x+y=\ldots \ldots \ldots \ldots \) (a) 15 (c) 2 (Itmailia 17) (d) zero (a) 15 (b) 21 (E1-Shartia 2.3) 4 If \( (2 a, b)=(3 b, 2) \), then \( \frac{a}{b}= \) (c) 7 (d) 10 (a) \( \frac{3}{2} \) (b) \( \frac{2}{3} \) (c) \( \frac{1}{2} \) (Luxar 24) 5. If \( \mathrm{n}(\mathrm{X})=2, \mathrm{n}(\mathrm{X} \times \mathrm{Y})=6 \), then \( \mathrm{n}\left(\mathrm{Y}^{2}\right)= \) \( \qquad \) (Giza 23) (a) 4 (b) 9 (c) 16 (d) 12 16 If \( X=\{3\} \), then \( X^{2}= \) \( \qquad \) (El-Shurkia i7) (3) 9 (b) \( (3,3) \) (c) \( \{9\} \) (d) \( \{(3,3)\} \) If \( X=\{1,2\} \quad, \quad Y=\{3,4\} \), then \( (3,4) \in \) (Qema 23) (a) \( X \times Y \) (b) \( \mathrm{Y} \times \mathrm{X} \) (c) \( \mathrm{X}^{2} \) (d) \( \mathrm{Y}^{2} \) 단 If \( \mathrm{X} \times \mathrm{Y}=\{(2,3)\} \), then \( \mathrm{X}^{2}=\ldots \ldots \) (El-Sharkia /S) (a) \( \{(4,9)\} \) (b) \( \{(4,3)\} \) (c) \( \{(2,2)\} \) (d) \( \{(2,9)\} \) 93 If \( f(x)=4 x+b, f(3)=15 \), then \( \mathrm{b}= \) (Et-Katyoubia 18) (a) 156 (b) 3 (c) 4 (d) -3 (10) If \( f: f(x)=\mathrm{n} x^{2}+2 x^{n}-3 \), then the set of possible values of \( n \) that make \( f \) a function of the second degree is \( \qquad \) (El-Dakailia 101 (a) \( \{2,3\} \) (b) \( \{1,-1\} \) (c) \( \{2,1,0\} \) (d) \( \{2,1\} \) \( 517: f(x)=5 \) is represented by a straight line parallel to the \( x \)-axis and passing through the point (Ismuilia 16) (a) \( (0,5) \) (b) \( (5,0) \) (c) \( (5,-5) \) (d) \( (0,0) \)

1.1. \( \frac{9^{n-1} \cdot 27^{3-2 n}}{81^{2-n}} \) \( 1.2 \sqrt{\frac{15^{x} \cdot 3^{x}}{9^{x+1} \cdot 5^{x-2}}} \) \( 1.3 \quad \frac{3.2^{n}-2^{n-2}}{2^{n+1}} \) \( 1.4 \quad \frac{4^{x+1}-4^{x-1}}{15.4^{-x+1} \cdot 4^{2 x-3}} \) \( 1.5 \quad \frac{5.3^{2 x-2}+3^{2 x}}{3^{2 x}-2.3^{2 x-2}} \)