Question

Evaluate:​
(iv) $2^5\times {15}^0+(-3{)}^3-(\frac{2}{7}{)}^{-2}$.

Answer 1

Given , $2^5\times {15}^0+(-3{)}^3-(\frac{2}{7}{)}^{-2}$.
On further simplification ,we have:
$2^5\times {15}^0+(-3{)}^3-(\frac{2}{7}{)}^{-2}$
$=2\times 2\times 2\times 2\times 2\times 1+(-3)\times (-3)\times (-3)-\left(\frac{7}{2}\right)\times \frac{7}{2}$
[$\because$ $a^0=1,a^{-m}=\frac{1}{a^m}$]

$=32\times 1-27-\frac{49}{4}$
$=\frac{32\times 4}{1\times 4}-\frac{27\times 4}{1\times 4}-\frac{49}{4\times 1}$ ($\because$ LCM $=4$)

$=\frac{128-108-49}{4}=\frac{-29}{4}=-7\frac{1}{4}$

Hence, $2^5\times {15}^0+(-3{)}^3-(\frac{2}{7}{)}^{-2}=-7\frac{1}{4}$ .