Question

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

A) 4 y cubed over 5 x to the fourth power
B) 4 y to the fourth power over 5 x cubed
C) 5 x to the fourth power over 4 y cubed
D) 5 x cubed over 4 y to the fourth power

Answer 1

the exponent symbol when typing is ^. so I so rewrite this for you.
(15x^8 / 24y^5) / (4x^4 / 8y^2)

I assumed you meant 8y squared because you said 8 squared.

now when we divide by a fraction, we can actually multiply by it's reciprocal and get the same thing. The word reciprocal really just means flip it over. so:

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

let's reduce the coefficients ( the numbers in front of the x and y) to make it easier.

We have 15/24 which can be reduced to 5/8
and 8/4 which is 2/1

so:
(5x^8 / 8y^5) * (2y^2 / x^4)

multiply numerator and denominator
(10x^8y^2) / (8x^4y^5)

now reduce coeffient. 10/8 is 5/4
reduce x: x^8/x^4 is x^4
reduce y: y^2/y^5 is 1/y^3

now put together
5x^4 / 4y^3

so C