<u>Question 1: Which expression is equivalent to (x^-4y/x^-9y^5)^-2 ? </u>
![(\frac{x^{-4} y}{x^{-9} y^{5} } )^{-2} \\\\ =(\frac{x^{-4}x^{9}}{ y^{5} y^{-1} } )^{-2} \\\\ =(\frac{x^{9-4}}{ y^{5-1}} )^{-2} \\\\ =(\frac{x^{5}}{ y^{4}} )^{-2} \\\\ =(\frac{y^{4}}{x^{5}} )^{2} \\\\ =\frac{y^{4*2}}{x^{5*2}} \\\\ =\frac{y^{8}}{x^{10}}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bx%5E%7B-4%7D%20y%7D%7Bx%5E%7B-9%7D%20y%5E%7B5%7D%20%7D%20%29%5E%7B-2%7D%20%5C%5C%5C%5C%0A%3D%28%5Cfrac%7Bx%5E%7B-4%7Dx%5E%7B9%7D%7D%7B%20y%5E%7B5%7D%20y%5E%7B-1%7D%20%7D%20%29%5E%7B-2%7D%20%5C%5C%5C%5C%0A%3D%28%5Cfrac%7Bx%5E%7B9-4%7D%7D%7B%20y%5E%7B5-1%7D%7D%20%29%5E%7B-2%7D%20%5C%5C%5C%5C%0A%3D%28%5Cfrac%7Bx%5E%7B5%7D%7D%7B%20y%5E%7B4%7D%7D%20%29%5E%7B-2%7D%20%5C%5C%5C%5C%0A%3D%28%5Cfrac%7By%5E%7B4%7D%7D%7Bx%5E%7B5%7D%7D%20%29%5E%7B2%7D%20%5C%5C%5C%5C%0A%3D%5Cfrac%7By%5E%7B4%2A2%7D%7D%7Bx%5E%7B5%2A2%7D%7D%20%5C%5C%5C%5C%0A%3D%5Cfrac%7By%5E%7B8%7D%7D%7Bx%5E%7B10%7D%7D)
Hence, option A is correct i.e.
.
<u>Question 2: Which expression is equivalent to 28p^9q^-5/12p^-6q^7 ?</u>
![\frac{28 p^{9} q^{-5} }{12 p^{-6} q^{7} } \\\\ =\frac{28 p^{9} p^{6} }{12 q^{7} q^{5} } \\\\ =\frac{28 p^{9+6} }{12 q^{7+5} } \\\\ =\frac{28 p^{15} }{12 q^{12} } \\\\ =\frac{7 p^{15} }{3 q^{12} }](https://tex.z-dn.net/?f=%5Cfrac%7B28%20p%5E%7B9%7D%20q%5E%7B-5%7D%20%7D%7B12%20p%5E%7B-6%7D%20q%5E%7B7%7D%20%7D%20%5C%5C%5C%5C%0A%3D%5Cfrac%7B28%20p%5E%7B9%7D%20p%5E%7B6%7D%20%7D%7B12%20q%5E%7B7%7D%20q%5E%7B5%7D%20%7D%20%5C%5C%5C%5C%0A%3D%5Cfrac%7B28%20p%5E%7B9%2B6%7D%20%7D%7B12%20q%5E%7B7%2B5%7D%20%7D%20%5C%5C%5C%5C%0A%3D%5Cfrac%7B28%20p%5E%7B15%7D%20%7D%7B12%20q%5E%7B12%7D%20%7D%20%5C%5C%5C%5C%0A%3D%5Cfrac%7B7%20p%5E%7B15%7D%20%7D%7B3%20q%5E%7B12%7D%20%7D)
Hence, option B is correct i.e.
.
<u>Question 3: Which expression is equivalent to (5ab)^3/30a^-6b^-7 ? </u>
![\frac{(5ab)^{3} }{30 a^{-6} b^{-7} } \\\\ =\frac{125 a^{3} b^{3} }{30 a^{-6} b^{-7} } \\\\ =\frac{125 a^{3} b^{3} a^{6} b^{7} }{30} \\\\ =\frac{25 a^{3+6} b^{3+7} }{6} \\\\ =\frac{25 a^{9} b^{10} }{6}](https://tex.z-dn.net/?f=%5Cfrac%7B%285ab%29%5E%7B3%7D%20%7D%7B30%20a%5E%7B-6%7D%20b%5E%7B-7%7D%20%7D%20%5C%5C%5C%5C%0A%3D%5Cfrac%7B125%20a%5E%7B3%7D%20b%5E%7B3%7D%20%7D%7B30%20a%5E%7B-6%7D%20b%5E%7B-7%7D%20%7D%20%5C%5C%5C%5C%0A%3D%5Cfrac%7B125%20a%5E%7B3%7D%20b%5E%7B3%7D%20a%5E%7B6%7D%20b%5E%7B7%7D%20%7D%7B30%7D%20%5C%5C%5C%5C%0A%3D%5Cfrac%7B25%20a%5E%7B3%2B6%7D%20b%5E%7B3%2B7%7D%20%7D%7B6%7D%20%5C%5C%5C%5C%0A%3D%5Cfrac%7B25%20a%5E%7B9%7D%20b%5E%7B10%7D%20%7D%7B6%7D)
Hence, option D is correct i.e.
.