Question

Please solve 1 & 2 fast

Answer 1

SOLUTION :-

$\frac{4}{(216) {}^{ - \frac{2}{3} } } + \frac{1}{(256) {}^{ \frac{ - 3}{4} } } + \frac{ 2}{(243) {}^{ \frac{ - 1}{5} } }$

Here ,

• 216 can be written as 6³
• 256 can be written as 2⁸
• 243 can be written as 3⁵

Lets simplify !

$\frac{4}{((6) {}^{3}) \frac{ - 2}{3} } + \frac{1}{((2) {}^{8}) \frac{ - 3}{4} } + \frac{2}{((3) {}^{5}) {}^{ \frac{ - 1}{5} } }$

By exponents and laws

$(a {}^{m} ) {}^{n} = a {}^{mn}$

$\frac{4}{6 {}^{3 \times \frac{ - 2}{3} } } + \frac{1}{2 {}^{8} { \times \frac { - 3}{4} }^{} } + \frac{2}{3 {}^{5} { \times \frac{ - 1}{5} }^{} }$

$\frac{4}{6 { }^{ - 2} } + \frac{1}{2 {}^{ - 6} } + \frac{2}{3 {}^{ - 1} }$

$\frac{1}{a {}^{ - n} } = a {}^{n}$

$a {}^{ - n} = \frac{1}{a {}^{n} }$

$\frac{4}{ \frac{1}{6 {}^{2} } } + \frac{1}{ \frac{1}{2 {}^{6} } } + \frac{1}{ \frac{2}{3} }$

$6 {}^{2} \times 4 + 2 {}^{6} \times 1 + 3 \times 2$

$36 \times 4 + 64 + 6$

$144 + 64 + 6$

$214$

_____________________________

2)

$( \frac{64}{125} ) {}^{ \frac{ - 2}{3} } + (\frac{256}{625} ) {}^{ \frac{ - 1}{4} } + (\frac{3}{7} ) {}^{0}$

• 64 can be written as 4³
• 125 can be written as 5³
• 256 can be written as 4⁴
• 625 can be written as 5⁴
• anything power 0 is 1

$( \frac{4 {}^{3} }{5 {}^{3} } ) {}^{ \frac{ - 2}{3} } +( \frac{4 {}^{4} }{5 {}^{4} } ) {}^{ \frac{ - 1}{4} } + 1$

$\frac{a {}^{x} }{b {}^{x} } = ( \frac{a}{b} ) {}^{x}$

$( (\frac{4}{5} ) {}^{3} ) \frac{ - 2}{3} + ((\frac{4}{5} ) {}^{4} ) {}^{ \frac{ - 1}{4} } + 1$

$( \frac{4}{5} ) {}^{ - 2} + (\frac{4}{5} ) {}^{ - 1} + 1$

$\frac{1}{( \frac{4}{5}) {}^{2} } + \frac{1}{ \frac{4}{5} } + 1$

$\frac{5 {}^{2} }{4 {}^{2} } + \frac{5}{4} + 1$

$\frac{25}{16} + \frac{5}{4} + 1$

LCM of 4, 16 is 16

$\frac{25 + 20 + 16}{16}$

$\frac{61}{16}$