Question

11. Simplify [ ( 1/3 )^ -2 - ( 1/2 )^ -3 + ( 1/4 )^ -1 ]^ ÷ 5^ -2​

Answer 1

Step-by-step explanation:

0.3 ^-2

-0.6

0.5^-3

-1.5

0.2^-1

0.2.

5^-2

= 0.23

Answer 2

Required question :

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

S O L U T I O N :

$\longmapsto\tt{\color{red}\frac{ (\frac{3}{1} )^{ 2} - ( \frac{2}{1})^{ 3} + ( \frac{4}{1})^{ 1} }{5 ^{ - 2} }}$

$\longmapsto\tt{\color{orange}\frac{ (3)^{ 2} - ( 2)^{ 3} + ( 4)^{ 1} }{5 ^{ - 2} }}$

$\longmapsto \tt{\color{lightpink}\frac{ \: 9 \: - \: 8 \: + \: 4 }{5 ^{ - 2} }}$

$\longmapsto \tt{\color{lightgreen}(5{ \: \div \frac{1}{5}) ^{2} }}$

$\longmapsto \tt{\color{blue}(5{ \: \times \frac{5}{1}) ^{2} }}$

$\longmapsto \tt{\color{purple}(25)^{2} }$

$\longmapsto \tt{\color{deeppink}625 \: or \: (25)^{2} }$

$\therefore \tt{\color{darkblue}625 \: or \: (25)^{2} \: is \: the \: answer.} \:$

More information :

• There are 6 laws of exponents :-

1) $\pmb{{a}^{3} \times {a}^{4} = {a}^{3 + 4} = {a}^{7} }$

2) $\pmb{ \frac{a ^{5} }{a ^{3} } = {a}^{5 - 3} = {a}^{2} }$

3) $\pmb{( {a}^{m} )^{n} )^{p} ) = {a}^{mnp} }$

4) $\pmb{(ab) ^{m} = {a}^{m} \times {b}^{m} or \: (a \div b)^{m} = {a}^{m} \div {b}^{m} }$

5) $\pmb{ {x}^{0} = 1}$

6) $\pmb{( \frac{a}{b} ) ^{ - m} = ( \frac{b}{a} ) ^{m}}$