Question

What is the simplified form of 24 y to the fifth power over 15 x to the eighth power divided by 8 y squared over 4 x to the fourth power?

Answer 1

`(4y^3)/(5x^4)`

Explanation:

Given phrase,

24 y to the fifth power over 15 x to the eighth power divided by 8 y squared over 4 x to the fourth power

`\implies (24y^5)/(15x^8)/ (8y^2)/(4x^4)`

`=(24y^5)/(15x^8)* (4x^4)/(8y^2)` ( Division of fractions )

`=(24y^5* 4x^4)/(15x^8* 8y^2)` ( Multiplication of fractions )

`=(96x^4y^5)/(120x^8y^2)`

`=(4)/(5) x^4y^5 x^(-8) y^(-2)` (
`a^m=(1)/(a^(-m))` )

`=(4)/(5)x^(-4)y^(3)` (
`a^m.a^n=a^(m+n)` )

`=(4y^3)/(5x^4)`