Question

Simplify and give reasons:
${\left(\frac{1}{2}\right)}^{-3}\times {\left(\frac{1}{4}\right)}^{-3}\times {\left(\frac{1}{5}\right)}^{-3}$

• A. ${40}^3$
• B. ${40}^{-3}$
• C. ${40}^6$
• D. None of these

Answer 1

The correct option is A ${40}^3$

we know,

$(\frac{a}{b}{)}^{-m}=(\frac{b}{a}{)}^m$

So,

$(\frac{1}{2}{)}^{-3}=(\frac{2}{1}{)}^3=2^3$

$(\frac{4}{1}{)}^{-3}=(\frac{4}{1}{)}^3=4^3$

$(\frac{5}{1}{)}^{-3}=(\frac{5}{1}{)}^3=5^3$

now we know,

\$a^m\ast b^m\ast c^m=(abc{)}^m$

$⟹(2{)}^3\ast (4{)}^3\ast (5{)}^3$

$=(40{)}^3$