What is factor ((4r^{-3}t^2)/(8rt^{-1)})^{-2} ?

The solution to factor ((4r^{-3}t^2)/(8rt^{-1)})^{-2} is (4r^8)/(t^6)

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factor ((4r^{-3}t^2)/(8rt^{-1)})^{-2}

factor

(\frac{4 r ^{- 3} t ^{2}}{8 r t ^{- 1}})^{- 2}

\frac{4 r ^{8}}{t ^{6}}

Solution steps

(\frac{4 r ^{- 3} t ^{2}}{8 r t ^{- 1}})^{- 2}

\frac{4 r ^{- 3} t ^{2}}{8 r t ^{- 1}} = \frac{t ^{3}}{2 r ^{4}}

= (\frac{t ^{3}}{2 r ^{4}})^{- 2}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{( \frac{t ^{3}}{2 r ^{4}} ) ^{2}}

Apply exponent rule:

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

(\frac{t ^{3}}{2 r ^{4}})^{2} = \frac{( t ^{3} ) ^{2}}{( 2 r ^{4} ) ^{2}}

= \frac{1}{\frac{( t ^{3} ) ^{2}}{( 2 r ^{4} ) ^{2}}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(2 r^{4})^{2} = 2^{2} (r^{4})^{2}

= \frac{1}{\frac{( t ^{3} ) ^{2}}{2 ^{2} ( r ^{4} ) ^{2}}}

(t^{3})^{2} : t^{6}

= \frac{1}{\frac{t ^{6}}{2 ^{2} ( r ^{4} ) ^{2}}}

(r^{4})^{2} : r^{8}

= \frac{1}{\frac{t ^{6}}{2 ^{2} r ^{8}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{2 ^{2} r ^{8}}{t ^{6}}

2^{2} = 4

= \frac{4 r ^{8}}{t ^{6}}

\frac{x - 1}{1 + x} < - 2

6 (4 + 3 x) = 7 (x - 1) + 1

\frac{5}{3} \cdot \frac{2}{3}

\frac{104 i}{5 + i}

3 e^{x^{2}} - 1 > 73

What is factor ((4r^{-3}t^2)/(8rt^{-1)})^{-2} ?
The solution to factor ((4r^{-3}t^2)/(8rt^{-1)})^{-2} is (4r^8)/(t^6)