Question

Perform the indicated operations.

Answer 1

`(14d^(3))/(3b^(2))`

Explanation:

`(10ab)/(c^(3)d)` ÷
`(15ab^(3))/(7c^(3)d^(4))` =
`(10ab)/(c^(3)d)*(7c^(3)d^(4))/(15ab^(3))\\`

`=(2ab)/(c^(3)d)*(7c^(3)d^(4))/(3ab^(3))\\\\=(2*7*a^(1-1)*c^(3-3)*d^(4-1))/(3b^(3-1))\\\\=(14a^(0)*c^(0)*d^(3))/(3b^(2))\\\\=(14*1*1*d^(3))/(3b^(2))\\\\=(14d^(3))/(3b^(2))`

Hint:

`\frac{x^(m)}x^(n)=x^(m-n); m>n\\\\\\(x^m)/(x^(n))=(1)/(x^(n-m)),n>m\\\\x^(0) =1`