Question

Complete the equation. Answer as a fraction in its simplest form. 9xy x (2/3x)^3=(__/__)x^4y

Answer 1

Fill the blank with
`(8)/(3)`

Explanation:

Given

`9xy * ((2)/(3)x)^3 = (--/--)x^4y`

Required

Fill in the gaps

`9xy * ((2)/(3)x)^3 = (--/--)x^4y`

Open Brackets

`9xy * (2^3)/(3^3)x^3 = (--/--)x^4y`

`9xy * (8)/(27)x^3 = (--/--)x^4y`

Multiply xy and x^3

`9 * (8)/(27)x^4y = (--/--)x^4y`

`(9 * 8)/(27)x^4y = (--/--)x^4y`

Divide fraction by 9/9

`(8)/(3)x^4y = (--/--)x^4y`

By comparison, the blank will be filled with:

`(8)/(3)`

Hence, the solution to the question is:
`9xy * ((2)/(3)x)^3 = (8)/(3)x^4y`