Question

simplify this question ​

Answer 1

$\dashrightarrow\rm \dfrac{4^{-\frac{1}{2}} \times 2^{\frac{1}{2}} \times 2}{8 \times 8^{-\frac{1}{2}}}$

$\dashrightarrow\rm \dfrac{(2^2)^{-\frac{1}{2}} \times 2^{\frac{1}{2}} \times 2}{2^3 \times (2^3)^{-\frac{1}{2}}}$

$\rm since, (a^m)^n = a^{mn} \therefore \ ,$

$\dashrightarrow\rm \dfrac{2^{2 \times -\frac{1}{2}} \times 2^{\frac{1}{2}} \times 2}{2^3 \times 2^{3 \times -\frac{1}{2}}}$

$\dashrightarrow\rm \dfrac{2^{ -\frac{2}{2}} \times 2^{\frac{1}{2}} \times 2}{2^3 \times 2^{-\frac{3}{2}}}$

$\dashrightarrow\rm \dfrac{2^{ -1} \times 2^{\frac{1}{2}} \times 2}{2^3 \times 2^{-\frac{3}{2}}}$

$\rm since, a^m \times a^n= a^{m+n} \therefore \ ,$

$\dashrightarrow\rm \dfrac{2^{ -1+\frac{1}{2}+1}}{2^{3+(-\frac{3}{2})}}$

$\dashrightarrow\rm \dfrac{2^{\frac{1}{2}}}{2^{3-\frac{3}{2}}}$

$\dashrightarrow\rm \dfrac{2^{\frac{1}{2}}}{2^{\tfrac{6}{2}-\frac{3}{2}}}$

$\dashrightarrow\rm \dfrac{2^{\frac{1}{2}}}{2^{\frac{6-3}{2}}}$

$\dashrightarrow\rm \dfrac{2^{\frac{1}{2}}}{2^{\frac{3}{2}}}$

$\rm since, \dfrac{a^m}{ a^n}= a^{m-n} \therefore \ ,$

$\dashrightarrow\rm 2^{\frac{1}{2} - \frac{3}{2}}$

$\dashrightarrow\rm 2^{ \frac{1-3}{2}}$

$\dashrightarrow\rm 2^{ \frac{-2}{2}}$

$\dashrightarrow\rm 2^{ -1}$

$\dashrightarrow\bf \dfrac{1}{2}$

Answer:-

$\qquad\qquad\bigstar\boxed{\bf \dfrac{1}{2}}\bigstar$