Simplify- 64-1-2-32-4-5- -2 Marks-

(64)^ 1/2 ( 32)^ 4/5 = (2^6)^ 1/2 ( 2^5)^ 4/5 = (2)^6× 1/2 ( 2)^5× 4/5 = (2)^ 3 ( 2)^ 4 nbsp; nbsp; [1 Mark] = 12^3 1( 2)^4 = 18 116 = 18(1 12) = 18(12) =1 ...

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Byju's Answer

Standard VIII

Mathematics

Indices

Simplify: 64-...

Question

Simplify: $(64)^{- \frac{1}{2}} - (- 32)^{- \frac{4}{5}}$ . [2 Marks]

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Solution

$(64)^{- \frac{1}{2}} - (- 32)^{- \frac{4}{5}}$
$= (2^{6})^{- \frac{1}{2}} - (- 2^{5})^{- \frac{4}{5}}$
$= (2)^{6 \times - \frac{1}{2}} - (- 2)^{5 \times - \frac{4}{5}}$
$= (2)^{- 3} - (- 2)^{- 4}$
[1 Mark]

$= \frac{1}{2^{3}} - \frac{1}{(- 2)^{4}}$
$= \frac{1}{8} - \frac{1}{16}$
$= \frac{1}{8} (1 - \frac{1}{2})$
$= \frac{1}{8} (\frac{1}{2})$
$= \frac{1}{16}$
[1 Mark]

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Similar questions

Simplify $(32)^{\frac{1}{5}} + (- 7)^{0} + (64)^{\frac{1}{2}}$

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(i)

\frac{4 + \sqrt{5}}{4 - \sqrt{5}} + \frac{4 - \sqrt{5}}{4 + \sqrt{5}}

(ii)

\frac{1}{\sqrt{3} + \sqrt{2}} - \frac{2}{\sqrt{5} - \sqrt{3}} - \frac{3}{\sqrt{2} - \sqrt{5}}

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\frac{2 + \sqrt{3}}{2 - \sqrt{3}} + \frac{2 - \sqrt{3}}{2 + \sqrt{3}} + \frac{\sqrt{3} - 1}{\sqrt{3} + 1}

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\frac{2 \sqrt{6}}{\sqrt{2} + \sqrt{3}} + \frac{6 \sqrt{2}}{\sqrt{6} + \sqrt{3}} - \frac{8 \sqrt{3}}{\sqrt{6} + \sqrt{2}}

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(3) $10 + (- 5) - (- 4)$

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Q. Simplify

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(3 + \sqrt{3}) (2 + \sqrt{2})

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(3 + \sqrt{3}) (3 - \sqrt{3})

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[ 4 Marks ]

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Simplify: (64)−12−(−32)−45. [2 Marks]

(64)−12−(−32)−45 =(26)−12−(−25)−45 =(2)6×−12−(−2)5×−45 =(2)−3−(−2)−4 [1 Mark] =123−1(−2)4 =18−116 =18(1−12) =18(12) =116 [1 Mark]

Simplify: $(64)^{- \frac{1}{2}} - (- 32)^{- \frac{4}{5}}$ . [2 Marks]