Obtain the volume of rectangular boxes with the following length, breadth and height respectively.

(i) $5a, 3a^2, 7a^4$

(ii) $2p, 4q, 8r$

(iii) $xy, 2x^{2}y, 2x{y}^2$

(iv) $a, 2b, 3c$

(i) Consider the given length, breadth and height of the rectangular boxes as follows,

$5a, 3a^2, 7a^4$

The volume of rectangle $=l\times b\times h$.

 Then the volume of the rectangle box is as follows,

 $5a\times 3a^2\times 7a^4=(5\times 3\times 7) (a\times a^2\times a^4 ) = 105a^7$

Hence, the volume of the rectangle is $105a^7$.

(ii) Consider the given length, breadth and height of the rectangular boxes as follows,

$2p, 4q, 8r$

The volume of rectangle $=l\times b\times h$.

 Then the volume of the rectangle box is as follows,

 $2p\times 4q\times 8r = (2\times 4\times 8) (p\times q\times r)=64pqr$

Hence, the volume of the rectangle is $64pqr$.

(iii) Consider the given length, breadth and height of the rectangular boxes as follows,

$xy, 2x^{2}y, 2x{y}^2$

The volume of rectangle $=l\times b\times h$.

 Then the volume of the rectangle box is as follows,

 $xy\times 2x^{2}y\times 2x{y}^2 =(1\times 2\times 2)( x\times x^2\times x\times y\times y\times y^2 )=4x^4{y}^4$

Hence, the volume of the rectangle is $4x^4{y}^4$.

(iv) Consider the given length, breadth and height of the rectangular boxes as follows,

$a, 2b, 3c$

The volume of rectangle $=l\times b\times h$.

 Then the volume of the rectangle box is as follows,

 $a\times 2b\times 3c=(1\times 2\times 3) (a\times b\times c)=6abc$

Hence, the volume of the rectangle is $6abc$.