Question

$(0.5{)}^{12}>(0.75{)}^6$

• A. True
• B. False

Answer 1

The correct option is B False

Note that $(0.5{)}^{12}=(\frac{1}{2}{)}^{12}=\frac{1}{2^{12}}$ and $(0.75{)}^6=(\frac{3}{4}{)}^6=\frac{3^6}{4^6}=\frac{3^6}{(2^2{)}^6}=\frac{3^6}{2^{12}}$
Now, $\frac{(0.75{)}^6}{(0.5{)}^{12}}=\frac{\frac{3^6}{2^{12}}}{\frac{1}{2^{12}}}=\frac{3^6}{2^{12}}\times \frac{2^{12}}{1}=3^6>1$
$⟹(0.75{)}^6>(0.5{)}^{12}$