What is ((9^2)/(9^{-12)})((9^{-3})/((-9^9))) ?

The solution to ((9^2)/(9^{-12)})((9^{-3})/((-9^9))) is -81

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simplify ((9^2)/(9^{-12)})((9^{-3})/((-9^9)))

simplify

(\frac{9 ^{2}}{9 ^{- 12}}) (\frac{9 ^{- 3}}{( - 9 ^{9} )})

- 81

Solution steps

(\frac{9 ^{2}}{9 ^{- 12}}) (\frac{9 ^{- 3}}{( - 9 ^{9} )})

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

= 9^{2 - (- 12)} \cdot \frac{9 ^{- 3}}{- 9 ^{9}}

Apply rule

- (- a) = a

= 9^{2 + 12} \cdot \frac{9 ^{- 3}}{- 9 ^{9}}

Add the numbers:

2 + 12 = 14

= 9^{14} \cdot \frac{9 ^{- 3}}{- 9 ^{9}}

\frac{9 ^{- 3}}{- 9 ^{9}} = - \frac{1}{9 ^{12}}

= 9^{14} (- \frac{1}{9 ^{12}})

Remove parentheses:

(- a) = - a

= - 9^{14} \cdot \frac{1}{9 ^{12}}

Multiply fractions:

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

= - \frac{1 \cdot 9 ^{14}}{9 ^{12}}

Multiply:

1 \cdot 9^{14} = 9^{14}

= - \frac{9 ^{14}}{9 ^{12}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{9 ^{14}}{9 ^{12}} = 9^{14 - 12}

= 9^{14 - 12}

Subtract the numbers:

14 - 12 = 2

= - 9^{2}

9^{2} = 81

= - 81

(7 a^{2} b c^{3}) (4 ab c)

(x - 3)^{4}

\frac{- 78}{6}

(e^{- \frac{7}{12}})^{4} ln (e^{- \frac{7}{12}})

What is ((9^2)/(9^{-12)})((9^{-3})/((-9^9))) ?
The solution to ((9^2)/(9^{-12)})((9^{-3})/((-9^9))) is -81