Question

State True or False.

$(125{)}^{-\frac{2}{3}}÷(8{)}^{-\frac{2}{3}}=\frac{1}{99}$.

• A. True
• B. False

Answer 1

Answer: (B)

$(125{)}^{-\frac{2}{3}}÷(8{)}^{-\frac{2}{3}}$
$=(5^3{)}^{-\frac{2}{3}}÷(2^3{)}^{-\frac{2}{3}}$
$=(5{)}^{-\frac{6}{3}}÷(2{)}^{-\frac{6}{3}}$ [$\because (a^m{)}^n=a^{m\times n}$]
$=(5{)}^{-2}÷(2{)}^{-2}$

$=\frac{1}{5^2}÷\frac{1}{2^2}$ [$\because a^{-m}=\frac{1}{a^m},a\ne 0$]

$=\frac{1}{25}÷\frac{1}{4}$

$=\frac{1}{25}\times \frac{4}{1}$

$=\frac{4}{25}$

Hence, the given statement is false.