Question

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

Answer 1

15x^5 4x^2
--------- / -------
24 y^8 8 y^4

invert the second fraction:-

15x^5 8y^4
------- * ------
24y^8 4 x^2


= 5 x^3
--------
4 y^4

Answer 2

Simplified form:
`\Rightarrow (5x^(3))/(4y^(4))`

Explanation:

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

Numerator: "15 x to the fifth power over 24 y to the eighth power"

`\Rightarrow (15x^5)/(24y^8)`

Denominator: "4 x squared over 8 y to the fourth power"

`\Rightarrow (4x^2)/(8y^4)`

Now we simplify numerator and denominator using exponent law.

Exponent Law:

`a^m\cdot a^n=a^(m+n)`

`a^m/ a^n=a^(m-n)`

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

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

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

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

`\Rightarrow (5x^(5-2))/(4y^(8-4))`

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