Question

evaluate 36 and half minus 36 minus root 2 upon 36

Answer 1

$\huge{\pink{\underline{\ulcorner{Solution}\urcorner}}}$

$(A)\:\frac{36^{\frac{1}{2}} - 36^{-\sqrt2}}{36^{-\frac{5}{2}}}$

$\implies \frac{6^{2\times\frac{1}{2}} - 6^{2\times-\frac{2}{2}}}{6^{2\times-\frac{5}{2}}}$

$\implies\frac{6^{\cancel{2}\times\frac{1}{\cancel2}} - 6^{-\cancel2\times\frac{2}{\cancel2}}}{6^{\cancel{2}\times-\frac{5}{\cancel2}}}$

$\implies \frac{6-6^{-2}}{6^{-5}}\\\\\implies\frac{\frac{6×6-1}{6}}{6^{-5}}$

$\implies \frac{(36-1)6^{5}}{6}\\\implies (36-1)6^4\\\implies(35)6^4$

$\red{\underline{Answer}}$

$\implies 45360$

Answer 2

Hello!

$\dfrac{36^{\tfrac{1}{2}} - 36^{-\sqrt{2}}}{36^{-\tfrac{5}{2}}} \\ \\ \implies \dfrac{6^{2 \times \tfrac{1}{2}} - 6^{2 \times -\sqrt{2}}}{6^{2 \times -\tfrac{5}{2}}} \\ \\ \implies \dfrac{6-6^{-2}}{6^{-5}} \\ \\ \implies \dfrac{(36-1)6^{5}}{6} \\ \\ \implies (36-1)6^{4} \\ \\ \implies 6^{4} \times 35 = \boxed{\red{\bf{45360}}}$

Cheers!