Simplify and give reasons- 3 4 -3

The correct option is A 6427 Given, (34)^ 3 we know that, (ab)^ m=(ba)^m so, =(43)^3 =4^33^3 =6427 ...

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Byju's Answer

Standard XII

Mathematics

Implicit Differentiation

Simplify and ...

Question

Simplify and give reasons:
${(\frac{3}{4})}^{- 3}$

\frac{64}{27}

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\frac{- 64}{27}

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\frac{4}{27}

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None of these

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Solution

The correct option is A $\frac{64}{27}$
Given,

$(\frac{3}{4})^{- 3}$

we know that,

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

so,

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

$= \frac{4^{3}}{3^{3}}$

$= \frac{64}{27}$

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Similar questions

Q. Simplify :

\sqrt[3]{\frac{64}{27}}

Q. Simplify

(27)^{\frac{- 2}{3}} \div (64)^{\frac{- 2}{3}}

is---

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. 3, 10, 27, 4, 16, 64, 5, 25, 125

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 and give reasons:(34)−3

The correct option is A 6427Given,(34)−3we know that,(ab)−m=(ba)mso,=(43)3=4333=6427

Simplify and give reasons:
${(\frac{3}{4})}^{- 3}$

The correct option is A $\frac{64}{27}$
Given,

$(\frac{3}{4})^{- 3}$

we know that,

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

so,

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

$= \frac{4^{3}}{3^{3}}$

$= \frac{64}{27}$