Question

What is the simplified form of 20 times x to the sixth power over 15 times y to the fifth power times the fraction 5 times y squared over 6 times x to the fourth power ?
a. 9 x squared over 10 y cubed
b. 9 x cubed over 10 y squared
c. 10 x cubed over 9 y squared
d. 10 x squared over 9 y cubed

Answer 1

In order to easily picture out the operation involving fractions, let's write it in an algebraic equation. So, the above description is written as

20x⁶/15y⁵ × 5y²/6x⁴

The first thing to do is to simplify the easiest terms: the constants. Just multiply all the constants on the numerator and all the constants on the denominator independently. The simplified constant becomes

(20*5)/(15*6) = 10/9

So, the equation to be solved now is 

10x⁶y²/9y⁵ x⁴

So, I also multiplied all the variables in the numerator and denominator independently, just like the constants. Then, you apply the laws of exponents. When you divide terms with exponents of the same value of the base, you subtract the exponent on the numerator minus the denominator. It goes like this:

10/9 * x⁶⁻⁴*y²⁻⁵ = 10/9*x²y⁻³

Now, when the exponent as written to the power of a negative exponent, just simply take its reciprocal to make it positive. So, the final answer is

10x²/9y³ or that is letter D.