Question

After simplication $5^{-4}\times (243{)}^{-\frac{2}{3}}÷(25{)}^{-\frac{1}{2}}$,the answer is 25

State true or false:

• A. True
• B. False

Answer 1

The correct option is B False

$5^{-4}\times (243{)}^{-\frac{2}{3}}÷(25{)}^{-\frac{1}{2}}$
$=5^{-4}\times (3^5{)}^{-\frac{2}{3}}÷(5^2{)}^{-\frac{1}{2}}$
$=5^{-4}\times (3{)}^{-\frac{2\times 5}{3}}÷(5{)}^{-\frac{2}{2}}$
$=5^{-4}\times (3{)}^{-\frac{10}{3}}÷(5{)}^{-1}$
$=5^{-4-(-1)}\times (3{)}^{-\frac{10}{3}}$
$=5^{-3}\times (3{)}^{-\frac{10}{3}}$