Question

State true or false:

$(\frac{2}{3}{)}^4\times (\frac{27}{8}{)}^{-2}=\frac{4}{9}$

• A. True
• B. False

Answer 1

The correct option is B False

$(\frac{2}{3}{)}^4\times (\frac{27}{8}{)}^{-2}$

$=(\frac{2}{3}{)}^4\times (\frac{3^3}{2^3}{)}^{-2}$

$=(\frac{2}{3}{)}^4\times (\frac{3}{2}{)}^{3\times (-2)}$

$=(\frac{2}{3}{)}^4\times (\frac{3}{2}{)}^{(-6)}$

$=(\frac{2}{3}{)}^4\times (\frac{2}{3}{)}^6$

$=(\frac{2}{3}{)}^{(4+6)}$

$=(\frac{2}{3}{)}^{10}$

The given statement is false.