NCERT Solutions for Chapter: Number Systems, Exercise 3: Exercise

Represent geometrically the following number on the number line:

$\sqrt{4.5}$

Simplify the following:
${\left(1^3+2^3+3^3\right)}^{\frac{1}{2}}$

Simplify the following:
${\left(\frac{3}{5}\right)}^4{\left(\frac{8}{5}\right)}^{-12}{\left(\frac{32}{5}\right)}^6$

Simplify the following:
${\left(\frac{1}{27}\right)}^{\frac{-2}{3}}$

Simplify the following:
${\left[{\left((625{)}^{-\frac{1}{2}}\right)}^{\frac{-1}{4}}\right]}^2$

Find the value of $k$ of the given $\frac{9^{\frac{1}{3}}\times {27}^{-\frac{1}{2}}}{3^{\frac{1}{6}}\times 3^{-\frac{2}{3}}}=k^{\frac{-1}{3}}$

Find the value of given expression,
${64}^{-\frac{1}{3}}\left[{64}^{\frac{1}{3}}-{64}^{\frac{2}{3}}\right]$

Simplify the following:
$\frac{8^{\frac{1}{3}}\times {16}^{\frac{1}{3}}}{{32}^{-\frac{1}{3}}}$