Question

Evaluate: $\frac{7^{-5}\times 49\times 21}{{14}^2\times 7^{-3}}$

• A. $-\frac{28}{3}$
• B. $-\frac{3}{28}$
• C. $\frac{3}{28}$
• D. $\frac{28}{3}$

Answer 1

The correct option is C $\frac{3}{28}$

$\frac{7^{-5}\times 49\times 21}{{14}^2\times 7^{-3}}$
$=\frac{7^{-5}\times 7^2\times 7\times 3}{{(7\times 2)}^2\times 7^{-3}}$
$=\frac{7^{-5+2+1}\times 3}{7^2\times 4\times 7^{-3}}$
$=\frac{7^{-2}\times 3}{7^{2-3}\times 4}$
$=\frac{7^{-2-(-1)}\times 3}{4}$
$=7^{-1}\times \frac{3}{4}$
$=\frac{1}{7}\times \frac{3}{4}$
$=\frac{3}{28}$

Hence, option $C$ is correct.