Question

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Answer 1

$(f) \: ( {6}^{2} \times {3}^{ - 2} )( {6}^{2} \div {3}^{ - 2} )$

$\sf \colorbox{pink} {Ans. (f)}$

$= \left( {6}^{2} \times \frac{1}{ {2}^{2} } \right) \] \left( {6}^{2} \div \frac{1}{ {3}^{2} } \right) \]\[ \left[ {a}^{ - m} = \frac{1}{ {a}^{m} } \right] \]$

$= \left( 6 \times 6 \times \frac{1}{3 \times 3} \right) \](36 \times 9)$

$= 4 \times 9 \times 36 = 36 \times 36 = 1296$

$(g) \: {5}^{0} + {3}^{0} - {2}^{0}$

$\sf \colorbox{pink} {Ans. (g)}$

$= {5}^{0} + {3}^{0} - {2}^{0}$

$= 1 + 1 - 1$

$= 1$

$(i) \: \left( \frac{ {a}^{3} {b}^{2} }{ {ab}^{ 3} } \right) \] {}^{ - 3}$

$\sf \colorbox{pink} {Ans. (i)}$

$= \left( \frac{ {a}^{3} {b}^{2} }{ {ab}^{ 3} } \right) \] {}^{ - 3}$

$= ( {a}^{2} \times {b}^{2} {)}^{ - 3}$

$= \left( \frac{ {b}^{2} }{a} \right) \] {}^{3}$

$(j) \: \[ \left[ { \left( \frac{1}{2} \right) \]}^{3} \right] \] {}^{2} \times { \left( \frac{1}{2} \right) \]}^{ - 2} \times {2}^{ - 1} \times 6$

$\sf \colorbox{pink} {Ans. (j)}$

$= \[ \left[ { \left( \frac{1}{2} \right) \]}^{3} \right] \] {}^{2} \times { \left( \frac{1}{2} \right) \]}^{ - 2} \times {2}^{ - 1} \times 6$

$= \[ \left[ { \left( \frac{1}{2} \right) \]}^{6} \right] \times {2}^{2} \times \frac{1}{2} \times 6$

$= \frac{1}{ {2}^{6} } \times 2 \times 6$

$= \frac{1}{64} \times 12$

$= \frac{3}{16}$

$(k) \: ( {3}^{0} + {2}^{0} ) + ( {3}^{0} - {2}^{0} )$

$\sf \colorbox{pink} {Ans. (k)}$

$= ( {3}^{0} + {2}^{0} ) + ( {3}^{0} - {2}^{0} )$

$= (1 - 1)(1 + 1) \: [As, {a}^{0} = 1,a≠0]$

$= 0 \times 2 = 0$

$\\ \\ \\ \\ \\ \sf \colorbox{gold} {\red(ANSWER ᵇʸ ⁿᵃʷᵃᵇ⁰⁰⁰⁸}$