Question

How do you divide and simplify `\frac { 2x ^ { 5} } { 9y ^ { 2} } \div \frac { 4y ^ { - 3} } { 9x ^ { - 8} }`?

Answer 1

`\frac { y }{ 2x ^ { 3} }`

Explanation:

`\frac { 2x ^ { 5} } { 9y ^ { 2} } \div \frac { 4y ^ { - 3} } { 9x ^ { - 8} }`

`\frac { 2x ^ { 5} } { 9y ^ { 2} } \times \frac { 9x ^ { - 8} } { 4y ^ { - 3} }`

(Turn the division sign in the expression into a multiplication sign)

`\frac { x ^ { 5} } { y ^ { 2} } \times \frac { x ^ { - 8} } { 2y ^ { - 3} }`

(Simplify the expression)

`\frac { x ^ { 5} } { y ^ { 2} } \times \frac { y ^ { 3 } }{ 2x ^ { 8} }`

(Turn the negative exponents into a positive value)

`\therefore \frac { y }{ 2x ^ { 3} }`

(Simplify the resulting expression which gives the fully simplified answer)