What is ((pq^3)^3(4p^2q)^2)/((2pq^2)^3) ?

The solution to ((pq^3)^3(4p^2q)^2)/((2pq^2)^3) is 2p^4q^5

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simplify ((pq^3)^3(4p^2q)^2)/((2pq^2)^3)

simplify

\frac{( p q ^{3} ) ^{3} ( 4 p ^{2} q ) ^{2}}{( 2 p q ^{2} ) ^{3}}

2 p^{4} q^{5}

Solution steps

\frac{( p q ^{3} ) ^{3} ( 4 p ^{2} q ) ^{2}}{( 2 p q ^{2} ) ^{3}}

Simplify

(4 p^{2} q)^{2} : 4^{2} p^{4} q^{2}

= \frac{( p q ^{3} ) ^{3} \cdot 4 ^{2} p ^{4} q ^{2}}{( 2 p q ^{2} ) ^{3}}

Simplify

(2 p q^{2})^{3} : 2^{3} p^{3} q^{6}

= \frac{( p q ^{3} ) ^{3} \cdot 4 ^{2} p ^{4} q ^{2}}{2 ^{3} p ^{3} q ^{6}}

Factor

4^{2} : 2^{4}

= \frac{( p q ^{3} ) ^{3} \cdot 2 ^{4} p ^{4} q ^{2}}{2 ^{3} p ^{3} q ^{6}}

\frac{2 ^{4}}{2 ^{3}} = 2

= \frac{( p q ^{3} ) ^{3} \cdot 2 p ^{4} q ^{2}}{p ^{3} q ^{6}}

Simplify

\frac{p ^{4}}{p ^{3}} : p

= \frac{( p q ^{3} ) ^{3} \cdot 2 p q ^{2}}{q ^{6}}

Simplify

\frac{q ^{2}}{q ^{6}} : \frac{1}{q ^{4}}

= \frac{( p q ^{3} ) ^{3} \cdot 2 p}{q ^{4}}

Simplify

\frac{( p q ^{3} ) ^{3} \cdot 2 p}{q ^{4}} : 2 p^{4} q^{5}

= 2 p^{4} q^{5}

\frac{3}{5} \cdot \frac{7}{10}

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

csc (θ) sin (θ)

e^{1} - 2

0.45

What is ((pq^3)^3(4p^2q)^2)/((2pq^2)^3) ?
The solution to ((pq^3)^3(4p^2q)^2)/((2pq^2)^3) is 2p^4q^5