Question

find the value of the following-​

Answer 1

$( {2}^{ - 1} \times {4}^{ - 1} ) \div {2}^{ - 2} \\ = ( {2}^{ - 1} \times {2}^{2 \times - 1}) \div {2}^{ - 2} \\ = ( {2}^{ - 1} \times {2}^{ - 2} ) \div {2}^{ - 2} \\ = ( {2}^{ - 1 + ( - 2)} ) \div {2}^{ - 2} \\ =( {2}^{ - 1 - 2} ) \div {2}^{ - 2} \\ = {2}^{ - 3} \div {2}^{ - 2} \\ = {2}^{ - 3 - ( - 2)} \\ = {2}^{ - 3 + 2} \\ = {2}^{ - 1} = \frac{1}{2} = 0.5$

Hence the answer is 2^-1 or 1/2 or 5.

To know :-

• When two numbers are same and we have to multiply them, we add the powers of number.
• When two numbers are same and we have to subtract them, we subtract denominator's power from numerator's power.

• If a number has negative power so the number is 1/number^power means if 2^-2 = 1/2² = 1/4 = 0.25.

hope it helps.

Answer 2

$\Large{(\frac{1}{2}×(\frac{1}{4})÷2^{-2}}$

$\Large=(\frac{5}{2})^3×(\frac{3}{2})^2$

$\Large=(\frac{125}{8})×(\frac{27}{8})$

$=\fbox{\frac{3375}{64}}$