The correct option is B 43 #160; √(6427) =√(4^33^3) we know that, ∵(a^m)^n=a^mn =(4^33^3)^1/3 =43 ...

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Question

Simplify : $\sqrt[3]{\frac{64}{27}}$

\frac{4}{3}

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\frac{4}{5}

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\frac{2}{3}

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\frac{2}{5}

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Solution

The correct option is B $\frac{4}{3}$
$\sqrt[3]{\frac{64}{27}}$

$= \sqrt[3]{\frac{4^{3}}{3^{3}}}$

we know that,

$∵ (a^{m})^{n} = a^{m n}$

$= (\frac{4^{3}}{3^{3}})^{\frac{1}{3}}$

$= \frac{4}{3}$

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Similar questions

Q. Simplify:

5 \sqrt{3} + 2 \sqrt{27} + 4 \sqrt{\frac{1}{3}}

Simplify :

$(i) 8^{\frac{4}{3}} + 25^{\frac{3}{2}} - {(\frac{1}{27})}^{- \frac{2}{3}} (i i) [(64)^{- 2}]^{- 3} \div [{(- 8)^{2}}^{3}]^{2} (i i i) (2^{- 3} - 2^{- 4}) (2^{- 3} + 2^{- 4})$

Q. Simplify:

4 \sqrt{3} (2 \sqrt{27} - 4 \sqrt{48}) - 5 \sqrt{3} (\sqrt{12} - 3 \sqrt{75})

Simplify:

(1) $2 + (- 4) - (+ 3)$

(2) $- 5 + 4 - (- 2)$

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

(4) $12 - (+ 6) + (- 3)$

(5) $- 15 + (- 4) - (+ 3)$

Q. Simplify:
(i)

(27)^{\frac{4}{3}} + (32)^{0.8} + (0.8)^{- 1}

(ii)

{(\frac{64}{125})}^{\frac{- 2}{3}} \div \frac{1}{{(\frac{256}{625})}^{\frac{1}{4}}} \times \frac{\sqrt{25}}{\sqrt[3]{64}}

(iii)

{⎡ ⎢ ⎢ ⎣ 5 {⎛ ⎜ ⎝ 8^{\frac{1}{3}} + 27^{\frac{1}{3}} ⎞ ⎟ ⎠}^{3} ⎤ ⎥ ⎥ ⎦}^{\frac{1}{4}}

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Simplify : 3√6427

The correct option is B 43 3√6427=3√4333we know that,∵(am)n=amn=(4333)13=43

Simplify : $\sqrt[3]{\frac{64}{27}}$

The correct option is B $\frac{4}{3}$
$\sqrt[3]{\frac{64}{27}}$

$= \sqrt[3]{\frac{4^{3}}{3^{3}}}$

we know that,

$∵ (a^{m})^{n} = a^{m n}$

$= (\frac{4^{3}}{3^{3}})^{\frac{1}{3}}$

$= \frac{4}{3}$