Question

Find the values of $x.$
(i) $3^x\times 3^{-2}=3^2$
(ii) $5^{-3}÷5^x=5^2$
(iii) ${\left(\frac{11}{5}\right)}^{-5}\times {\left(\frac{11}{5}\right)}^{-2}={\left(\frac{11}{5}\right)}^{x-9}$

• A. $i)-4ii)5iii)2$
• B. $i\left)4ii\right)-5iii)2$
• C. $i\left)1ii\right)-1iii)16$
• D. $i)-4ii)-5iii)-2$

Answer 1

Answer: (B)

$i\left)4ii\right)-5iii)2$

$\left(1\right)3^x\cdot 3^{-2}=3^2{3}^{x-2}=3^2\therefore x-2=2sox=4\left(2\right)5^{-3}÷5^x=5^2\left(\frac{5^{-3}}{5^x}\right)=5^2{5}^{-3-x}=5^2-3-x=2\therefore x=-3-2=-5\left(3\right)(\frac{11}{5}{)}^{-5}\cdot (\frac{11}{5}{)}^{-2}=\left(\frac{11}{5}{)}^{x-9}\right(\frac{11}{5}{)}^{-5-2}=(\frac{11}{5}{)}^{x-9}-7=x-9\therefore x=2$