Question

Mark (✓) against the correct answer
If ${\left(\frac{5}{12}\right)}^{-4}\times {\left(\frac{5}{12}\right)}^{3x}={\left(\frac{5}{12}\right)}^5,\mathrm{then}x=?$
(a) −1
(b) 1
(c) 2
(d) 3

Answer 1

(d) 3

$$\begin{gathered} {\left(\frac{5}{12}\right)}^{-4}\times {\left(\frac{5}{12}\right)}^{3x}={\left(\frac{5}{12}\right)}^5 \\ \Rightarrow {\left(\frac{5}{12}\right)}^{-4+3x}={\left(\frac{5}{12}\right)}^5 \\ \Rightarrow -4+3x=5 \\ \Rightarrow 3x=5+4=9 \\ \Rightarrow x=\frac{9}{3}=3 \end{gathered}$$