Question

$( \frac{3}{4} ) {}^{ - 2)3} =$
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Answer 1

Answer:

$\frac{4029}{729}$

Step-by-step explanation:

$(( \frac{3}{4} )^{ - 2})^{3} \\ = ) (\frac{3}{4} )^{ - 6} \\ = ) (\frac{4}{3} )^{6} \\ = ) \frac{4096}{729}$

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Answer 2

☆ By using laws of exponents, its easy to simplify this.

→ Using $((\frac{a}{b} )^{m})^{n} = \frac{a}{b}^{m*n}$ we get,

$((\frac{3}{4} )^{-2})^{3} \\\\(\frac{3}{4})^{-2*3}\\\\(\frac{3}{4})^{-6}$

→ Using $(a)^{-m} = (\frac{1}{a})^{m}$

$(\frac{3}{4})^{-6} =(\frac{4}{3})^{6}$

→Using $(\frac{a}{b})^{m} =\frac{x^{m} }{y^{m} }$

$(\frac{4}{3})^{6} \\\\\frac{4^{6} }{3^{6} }\\\\\frac{4096}{729}$

∴$((\frac{3}{4} )^{-2})^{3} =\frac{4^{6} }{3^{6} }$

                 ------✨HOPE IT HELPS✨------