Question

State whether the given statement is True or False.
${\left(\frac{-3}{5}\right)}^{100}=\frac{-3^{100}}{-5^{100}}$

Answer 1

To check: ${\left(\frac{-3}{5}\right)}^{100}=\frac{-3^{100}}{-5^{100}}$

We know that,
For any non-zero integers a and b and whole number m,
\(\left ( \dfrac{a}{b} \right )^{m}=a^m$÷$b^m\)
LHS: ${\left(\frac{-3}{5}\right)}^{100}=\frac{(-3{)}^{100}}{5^{100}}=\frac{3^{100}}{5^{100}}$
RHS: $\frac{-3^{100}}{-5^{100}}=\frac{3^{100}}{5^{100}}$
$\Rightarrow$ LHS = RHS
$\therefore {\left(\frac{-3}{5}\right)}^{100}=\frac{-3^{100}}{-5^{100}}$
Hence, the given statement is true.