What is ((4s^5t^{-7})/(-2s^{-2)t^4})^3 ?

The solution to ((4s^5t^{-7})/(-2s^{-2)t^4})^3 is -(8s^{21})/(t^{33)}

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simplify ((4s^5t^{-7})/(-2s^{-2)t^4})^3

simplify

(\frac{4 s ^{5} t ^{- 7}}{- 2 s ^{- 2} t ^{4}})^{3}

- \frac{8 s ^{21}}{t ^{33}}

Solution steps

(\frac{4 s ^{5} t ^{- 7}}{- 2 s ^{- 2} t ^{4}})^{3}

Apply exponent rule:

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

= \frac{( 4 s ^{5} t ^{- 7} ) ^{3}}{( - 2 s ^{- 2} t ^{4} ) ^{3}}

Simplify

(4 s^{5} t^{- 7})^{3} : \frac{64 s ^{15}}{t ^{21}}

= \frac{\frac{64 s ^{15}}{t ^{21}}}{( - 2 s ^{- 2} t ^{4} ) ^{3}}

Simplify

(- 2 s^{- 2} t^{4})^{3} : - \frac{8 t ^{12}}{s ^{6}}

= \frac{\frac{64 s ^{15}}{t ^{21}}}{- \frac{8 t ^{12}}{s ^{6}}}

Apply the fraction rule:

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

= - \frac{\frac{64 s ^{15}}{t ^{21}}}{\frac{8 t ^{12}}{s ^{6}}}

Divide fractions:

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

= - \frac{64 s ^{15} s ^{6}}{t ^{21} \cdot 8 t ^{12}}

Divide the numbers:

\frac{64}{8} = 8

= - \frac{8 s ^{15} s ^{6}}{t ^{21} t ^{12}}

8 s^{15} s^{6} = 8 s^{21}

= - \frac{8 s ^{21}}{t ^{21} t ^{12}}

t^{21} t^{12} = t^{33}

= - \frac{8 s ^{21}}{t ^{33}}

2 (2 x + 9) = 50

9 u^{2} - 4

(ab)^{4} - 81

(\frac{6 n ^{2}}{3 n})^{- 3}

(b - c)^{3} + (c - a)^{3} + (a - b)^{3}

What is ((4s^5t^{-7})/(-2s^{-2)t^4})^3 ?
The solution to ((4s^5t^{-7})/(-2s^{-2)t^4})^3 is -(8s^{21})/(t^{33)}