Question

State true or false.

After simplification $3^3\times (243{)}^{-\frac{2}{3}}\times 9^{-\frac{1}{3}}$ is equal to $\frac{1}{3}$.

• A. True
• B. False

Answer 1

The correct option is A True

$3^3\times (243{)}^{-\frac{2}{3}}\times 9^{-\frac{1}{3}}$

$=3^3\times (3{)}^{-\frac{10}{3}}\times 3^{-\frac{2}{3}}$ ........ $\because 243=3^5$

$=3^{3-\frac{10}{3}-\frac{2}{3}}$

$=3^{\frac{9-10-2}{3}}$

$=3^{\frac{-3}{3}}$

$=3^{-1}$

$=\frac{1}{3}$