ABC26GN1914 · Surds and Indices
Subject: General Aptitude · Chapter: Surds and Indices · Exam: 2010 · Marks: · Difficulty:
Simplified form of $\left[\left(\sqrt[5]{x^{-\frac{3}{5}}}\right)^{-\frac{5}{3}}\right]^{5}$ is
(a)$\frac{1}{x}$
(b)$x$
(c)$x^{-5}$
(d)$x^{5}$
Answer
Explanation
$\left[\left(\sqrt[5]{x^{-\frac{3}{5}}}\right)^{-\frac{5}{3}}\right]^{5}=\left[\left\{\left(x^{-\frac{3}{5}}\right)^{\frac{1}{5}}\right\}^{-\frac{5}{3}}\right]^{5}=\left[\left(\left\{\left(-\frac{3}{5}\right) \times \frac{1}{5}\right\}\right)^{-\frac{5}{3}}\right]^{5}$ $$\begin{aligned} & =\left[\left(x^{-\frac{3}{25}}\right)^{-\frac{5}{3}}\right]^{5}=\left[x^{\left.\left\{\left(-\frac{3}{25}\right) \times\left(-\frac{5}{3}\right)\right\}\right]^{5}}\right. \\ & =\left(x^{\frac{1}{5}}\right)^{5}=x^{\left(\frac{1}{5} \times 5\right)}=x \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
Open in whiteboard · Browse this chapter in the app