What is ((-6a^{-9}b^5)/(2a^2b^{-4)})^4 ?

The solution to ((-6a^{-9}b^5)/(2a^2b^{-4)})^4 is (81b^{36})/(a^{44)}

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simplify ((-6a^{-9}b^5)/(2a^2b^{-4)})^4

simplify

(\frac{- 6 a ^{- 9} b ^{5}}{2 a ^{2} b ^{- 4}})^{4}

\frac{81 b ^{36}}{a ^{44}}

Solution steps

(\frac{- 6 a ^{- 9} b ^{5}}{2 a ^{2} b ^{- 4}})^{4}

Apply exponent rule:

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

= \frac{( - 6 a ^{- 9} b ^{5} ) ^{4}}{( 2 a ^{2} b ^{- 4} ) ^{4}}

Simplify

(- 6 a^{- 9} b^{5})^{4} : \frac{1296 b ^{20}}{a ^{36}}

= \frac{\frac{1296 b ^{20}}{a ^{36}}}{( 2 a ^{2} b ^{- 4} ) ^{4}}

Simplify

(2 a^{2} b^{- 4})^{4} : \frac{16 a ^{8}}{b ^{16}}

= \frac{\frac{1296 b ^{20}}{a ^{36}}}{\frac{16 a ^{8}}{b ^{16}}}

Divide fractions:

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

= \frac{1296 b ^{20} b ^{16}}{a ^{36} \cdot 16 a ^{8}}

Divide the numbers:

\frac{1296}{16} = 81

= \frac{81 b ^{20} b ^{16}}{a ^{36} a ^{8}}

81 b^{20} b^{16} = 81 b^{36}

= \frac{81 b ^{36}}{a ^{36} a ^{8}}

a^{36} a^{8} = a^{44}

= \frac{81 b ^{36}}{a ^{44}}

2 a^{2} - 9 a - 45

- \frac{1}{2} (2) + 1

2 x + 1 \leq - 5

(a^{2} b c^{3})^{4} \cdot (b^{2} c)^{3}

\frac{5 - i}{3 + 4 i}

What is ((-6a^{-9}b^5)/(2a^2b^{-4)})^4 ?
The solution to ((-6a^{-9}b^5)/(2a^2b^{-4)})^4 is (81b^{36})/(a^{44)}