What is (-3/4)^{-2}*[(-9/16)^{-3}]^{-2} ?

The solution to (-3/4)^{-2}*[(-9/16)^{-3}]^{-2} is 59049/1048576

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simplify (-3/4)^{-2}*[(-9/16)^{-3}]^{-2}

simplify

(- \frac{3}{4})^{- 2} \cdot [(- \frac{9}{16})^{- 3}]^{- 2}

\frac{59049}{1048576}

Decimal Notation

0.05631 \dots

Solution steps

(- \frac{3}{4})^{- 2} ((- \frac{9}{16})^{- 3})^{- 2}

(- \frac{3}{4})^{- 2} = \frac{16}{9}

= \frac{16}{9} ((- \frac{9}{16})^{- 3})^{- 2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

((- \frac{9}{16})^{- 3})^{- 2} = (- \frac{9}{16})^{- 3 (- 2)}

= \frac{16}{9} (- \frac{9}{16})^{- 3 (- 2)}

- 3 (- 2) = 6

= \frac{16}{9} (- \frac{9}{16})^{6}

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

(- \frac{9}{16})^{6} = (\frac{9}{16})^{6}

= \frac{16}{9} (\frac{9}{16})^{6}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

(\frac{9}{16})^{6} = \frac{9 ^{6}}{1 6 ^{6}}

= \frac{16}{9} \cdot \frac{9 ^{6}}{1 6 ^{6}}

\frac{9 ^{6}}{1 6 ^{6}} = \frac{531441}{16777216}

= \frac{16}{9} \cdot \frac{531441}{16777216}

\frac{16}{9} \cdot \frac{531441}{16777216} = \frac{59049}{1048576}

= \frac{59049}{1048576}

0.15 \cdot 1 0^{- 3}

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0.15 \cdot 1 0^{- 6}

6 4^{(\frac{1}{9})} \cdot 8^{(\frac{1}{9})}

(\frac{2}{6})^{2} e^{- (\frac{2}{6})}

What is (-3/4)^{-2}*[(-9/16)^{-3}]^{-2} ?
The solution to (-3/4)^{-2}*[(-9/16)^{-3}]^{-2} is 59049/1048576