1. Află \( x \in \mathbb{N} \) dacă: (a) \( \frac{2 x+3}{x+1} \in \mathbb{N} \) (b) \( \frac{4 x+3}{3 x-1} \in \mathbb{N} \)

Simplify by using laws of indices: \( \frac{(81)^{n} 3^{5}-3^{4 n-1}(243)}{\left(9^{2 n}\right)\left(3^{3}\right)} \) Simplify by using laws of indices:: \( \frac{(243)^{\frac{3^{-2}(32)}{} 5^{-1}}}{\sqrt{(196)^{-1}}} \) Simplify by using laws of indices: \( \left(\frac{4 x^{9} y^{2} z^{-3}}{9 x^{-2} y^{-3}}\right)^{-3} \) Simnlify by using laws of indices: \( \sqrt[3]{b^{2}} \div \sqrt[5]{b} \)

7. Simplify by using 8. Simplify by using laws of indices: \( (c d)^{5} \div\left(c^{5} d 5\right)^{5} \) 9. Simplify by using laws of indices: \( \frac{\sqrt{(512)^{2 / 3 \times(49) 1 / 2}}}{(0.09)^{-1 / 2}} \) 10. Simplify by using laws of indices: \( \frac{(216)^{2 / 5} \times(25)^{1 / 2}}{(0.04)^{-2 / 2}} \) 11. Simplify by using laws of indices: \( \left(x^{2} y^{-3}\right) \times \sqrt[3]{8\left(x^{-3} y^{2}\right)} \) 12. A person earns a monthly salary of Rs 32,500 and receives an an

19. Expand: : \( (5 a-3 b)^{3} \)

2. Suppose y varies directly with \( x \). If \( x \) is 30 when \( y \) is 10 , what is \( x \) when \( y \) is 9 ? (D) 3 (1) 27 (C) 29 (D) \( \frac{300}{9} \) 3. Which equation represents a line with slope -2 and \( y \)-intercept 3 ? (D) \( 3 y=x-2 \) (C) \( 3 y=-2 x+1 \) (H) \( y=2 x-3 \) D \( y=-2 x+3 \) 8. What is the vertex of \( y=|x|-5 \) ? (A) \( (5,0) \) (B) \( (-5,0) \) (C) \( (0,5) \) (D) \( (0,-5) \) . The amount of a commission is directly proportional to the amount of a sale. A realior recelved a commlssion of \( \$ 48,000 \) on the male of an \( \$ 800,000 \) house. How much would the commission be on a \( \$ 650,000 \) bouse?

Simplify by using laws of indices: \( (c d)^{5} \div\left(c^{5} d 5\right)^{5} \) Simplify by using laws of indices: \( \frac{\sqrt{(512)^{2 / 5} \times(49)^{1 / 2}}}{(0.09)^{-1 / 2}} \) 0. Simplify by using laws of indices: \( \frac{\sqrt{(216)^{2 / 3} \times(25)^{1 / 2}}}{(0.04)^{-1 / 2}} \) 1. Simplify by using laws of indices: \( \left(x^{2} y^{-3}\right) \times \sqrt[3]{8\left(x^{-3} y^{2}\right)} \)