What is (((5p^3*q^3*r))/((6p*q^3*r^3)))^{-2} ?

The solution to (((5p^3*q^3*r))/((6p*q^3*r^3)))^{-2} is (36r^4)/(25p^4)

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simplify (((5p^3q^3r))/((6pq^3r^3)))^{-2}

simplify

(\frac{( 5 p ^{3} \cdot q ^{3} \cdot r )}{( 6 p \cdot q ^{3} \cdot r ^{3} )})^{- 2}

\frac{36 r ^{4}}{25 p ^{4}}

Solution steps

(\frac{5 p ^{3} q ^{3} r}{6 p q ^{3} r ^{3}})^{- 2}

Apply exponent rule:

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

(\frac{5 p ^{3} q ^{3} r}{6 p q ^{3} r ^{3}})^{- 2} = \frac{1}{( \frac{5 p ^{3} q ^{3} r}{6 p q ^{3} r ^{3}} ) ^{2}}

= \frac{1}{( \frac{5 p ^{3} q ^{3} r}{6 p q ^{3} r ^{3}} ) ^{2}}

Simplify

(\frac{5 p ^{3} q ^{3} r}{6 p q ^{3} r ^{3}})^{2} : \frac{25 p ^{4}}{36 r ^{4}}

= \frac{1}{\frac{25 p ^{4}}{36 r ^{4}}}

Apply the fraction rule:

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

= \frac{36 r ^{4}}{25 p ^{4}}

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What is (((5p^3*q^3*r))/((6p*q^3*r^3)))^{-2} ?
The solution to (((5p^3*q^3*r))/((6p*q^3*r^3)))^{-2} is (36r^4)/(25p^4)