Question

find the value of the following

➊ ( 2⁰ + 3-¹ ) × 3²
$\tt ➋ \: (3 ^{ - 1} \times {6}^{ - 1}) \div {3}^{ - 2}$
$\tt ➌ \: ( \frac{1}{3} ) ^{ - 2} + ( \frac{1}{4} ) ^{ - 2} + ( \frac{1}{5} ) ^{ - 2}$
$\tt ➍ \: ( {2}^{ - 1} + {3}^{ - 1} + {4}^{ - 1}) ^{0}$
$\tt ➎ \: [( \frac{ - 1}{3} ) ^{ - 2} ] ^{2}$
➏ [ { (-⅓) ²} -² ] -¹

[Also tell about exponent ( in additional information ಠಿ_ಠ )]

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＼(°o°)／ 30 points​

Answer 1

$\huge\rm { ☆_!! Question !_! ☆}$

find the value of the following:-

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$➊ \: \tt ( 2⁰ + 3 ^{ - 1} ) × 3²$

$⇢ \tt ( 1 + \dfrac{1}{3} ) × 9$

$⇢ \tt (\dfrac{3 + 1}{3} ) × 9$

$⇢ \tt (\dfrac{4}{ \cancel{3}} ) × { \cancel{9}} = 12$

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$\tt ➋ \: (3 ^{ - 1} \times {6}^{ - 1}) \div {3}^{ - 2}$

$\tt ⇢ \: ( \dfrac{1}{3} \times \dfrac{1}{6} ) \div \dfrac{1}{ {3}^{2} }$

$\tt ⇢ \: \dfrac{1}{18} \div \dfrac{1}{9}$

$\tt ⇢ \: \dfrac{ \cancel{1}}{18} \div \dfrac{9}{ \cancel{1}} = \dfrac{1}{2}$

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$➌ \: ( \dfrac{1}{3} ) ^{ - 2} + ( \dfrac{1}{4} ) ^{ - 2} + ( \dfrac{1}{5} ) ^{ - 2}$

$⇢ \tt {3}^{2} + {4}^{2} + {5}^{2}$

$⇢ \tt 9 + 16 + 25$

$⇢ \tt 50$

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$➍ \tt ( {2}^{ - 1} + {3}^{ - 1} + {4}^{ - 1}) ^{0}$

$⇢ \tt ( \dfrac{1}{2} + \dfrac{1}{3} + \dfrac{1}{4} ) ^{0}$

$⇢ \tt ( \dfrac{6 + 4 + 3}{12}) ^{0}$

$⇢ \tt ( \dfrac{13}{12}) ^{0} = 1$

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$➎ \tt [( \dfrac{ - 1}{3} ) ^{ - 2} ] ^{2}$

$⇢ \tt ( \dfrac{ - 1}{3} ) ^{ - 2} \times ^{2}$

$⇢ \tt ( \dfrac{ - 1}{3} ) ^{ 4} = ( \dfrac{ 3}{ - 1} ) ^{ 4}$

$⇢ \tt ( - 3 ) ^{ 4} = 81$

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➏ [ { (-⅓) ²} -² ] -¹

$⇢ \tt [ ( \dfrac{ - 1}{3} ) ^{2} ] ^{( - 2) \times ( - 1)} = [ (\dfrac{ - 1}{3} ) ^{2} ] ^{ - 2 }$

$⇢ \tt (\dfrac{ - 1}{3} ^{2} ) ^{2 \times 2} = (\dfrac{ - 1}{3} ^{2} ) ^{4}$

$⇢ \tt \dfrac{ (- 1) ^{4} }{(3) ^{4} } = \dfrac{1 }{81 }$

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⭐ ADDITIONAL INFORMATION ⭐

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» Repeated multiplication of a number/thing by itself can be shown by exponents.

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» For example, 2 x 2 x 2 x 2 x 2 = 25. Here '2', which is being multiplied by itself is called the base and '5' which tells the number of times 2 is being multiplied by itself is known as the exponent.

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» The number $\tt 2^{5}$ can be read as '2 raised to power 5'. The exponent is written higher than the base and its size is smaller than that of the base.

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» For any non - zero integers/rational numbers a and b, and whole numbers m and n

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$➊ \: \tt {a}^{m} \times {a}^{n} = a ^{m + n}$

$➋ \: \tt {a}^{m} \div {a}^{n} = a ^{m - n}$

$➌ \: \tt ({a}^{m} )^{n} = a ^{m n}$

$➍ \: \tt {a}^{m} \times {b} ^{m} = (ab) ^{m}$

$➎ \: \tt {a}^{m} \div {b} ^{m} = ( \dfrac{a}{b} ) ^{m}$

$➏ \: \tt {a}^{0} = 1$