What is ((4/9)^{-2})/((27/8)^{-3)} ?

The solution to ((4/9)^{-2})/((27/8)^{-3)} is 1594323/8192

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simplify ((4/9)^{-2})/((27/8)^{-3)}

simplify

\frac{( \frac{4}{9} ) ^{- 2}}{( \frac{27}{8} ) ^{- 3}}

\frac{1594323}{8192}

Decimal Notation

194.61950 \dots

Solution steps

\frac{( \frac{4}{9} ) ^{- 2}}{( \frac{27}{8} ) ^{- 3}}

(\frac{4}{9})^{- 2} = \frac{81}{16}

= \frac{\frac{81}{16}}{( \frac{27}{8} ) ^{- 3}}

(\frac{27}{8})^{- 3} = \frac{512}{19683}

= \frac{\frac{81}{16}}{\frac{512}{19683}}

Apply the fraction rule:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{81 \cdot 19683}{16 \cdot 512}

Multiply the numbers:

81 \cdot 19683 = 1594323

= \frac{1594323}{16 \cdot 512}

Multiply the numbers:

16 \cdot 512 = 8192

= \frac{1594323}{8192}

lo g_{\frac{1}{4}} (5)

\frac{75}{48}

ln (9)

12 = - 15 x - 6

\frac{4}{9} \cdot \frac{3}{2}

What is ((4/9)^{-2})/((27/8)^{-3)} ?
The solution to ((4/9)^{-2})/((27/8)^{-3)} is 1594323/8192