What is ((a^{-2}b^4c^5)/(a^{-4)b^{-4}c^3})^2 ?

The solution to ((a^{-2}b^4c^5)/(a^{-4)b^{-4}c^3})^2 is a^4b^{16}c^4

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simplify ((a^{-2}b^4c^5)/(a^{-4)b^{-4}c^3})^2

simplify

(\frac{a ^{- 2} b ^{4} c ^{5}}{a ^{- 4} b ^{- 4} c ^{3}})^{2}

a^{4} b^{16} c^{4}

Solution steps

(\frac{a ^{- 2} b ^{4} c ^{5}}{a ^{- 4} b ^{- 4} c ^{3}})^{2}

Apply exponent rule:

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

= \frac{( a ^{- 2} b ^{4} c ^{5} ) ^{2}}{( a ^{- 4} b ^{- 4} c ^{3} ) ^{2}}

Simplify

(a^{- 2} b^{4} c^{5})^{2} : \frac{b ^{8} c ^{10}}{a ^{4}}

= \frac{\frac{b ^{8} c ^{10}}{a ^{4}}}{( a ^{- 4} b ^{- 4} c ^{3} ) ^{2}}

Simplify

(a^{- 4} b^{- 4} c^{3})^{2} : \frac{c ^{6}}{a ^{8} b ^{8}}

= \frac{\frac{b ^{8} c ^{10}}{a ^{4}}}{\frac{c ^{6}}{a ^{8} b ^{8}}}

Divide fractions:

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

= \frac{b ^{8} c ^{10} a ^{8} b ^{8}}{a ^{4} c ^{6}}

Apply exponent rule:

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

\frac{c ^{10}}{c ^{6}} = c^{10 - 6}

= \frac{a ^{8} b ^{8} b ^{8} c ^{10 - 6}}{a ^{4}}

Subtract the numbers:

10 - 6 = 4

= \frac{a ^{8} b ^{8} b ^{8} c ^{4}}{a ^{4}}

Apply exponent rule:

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

\frac{a ^{8}}{a ^{4}} = a^{8 - 4}

= b^{8} b^{8} c^{4} a^{8 - 4}

Subtract the numbers:

8 - 4 = 4

= a^{4} b^{8} b^{8} c^{4}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

b^{8} b^{8} = b^{8 + 8}

= a^{4} b^{8 + 8} c^{4}

Add the numbers:

8 + 8 = 16

= a^{4} b^{16} c^{4}

3 \leq x + 10 < 18

\frac{x}{8} \geq - 1.5

\frac{17}{15} \cdot \frac{2}{11}

(- \frac{x ^{5}}{2})^{4}

\frac{3 m - 9}{4 m + 8} \cdot \frac{m ^{2} + 5 m + 6}{m ^{2} - 9}

What is ((a^{-2}b^4c^5)/(a^{-4)b^{-4}c^3})^2 ?
The solution to ((a^{-2}b^4c^5)/(a^{-4)b^{-4}c^3})^2 is a^4b^{16}c^4