Answer to the Math Problem of the Week for April 15, 2014

Question: One hundred twenty times a number x raised to the fifth power times another number y raised to the sixth power is divided by the quantity of eighty times the number y to the fourth power times another number z raised to the third power. What is this expression in simplest form?

Answer:
3x^5y^2
   2z^3
First, we have to translate the word expression into the number expression.

120x^5y^6  or   120 * x^5 * y^6
 80y^4z^3          80  * z^3 * y^4

Simplify each of the like terms: 

• Both 120 and 80 can be divided by 40 to reduce down to 3/2.
• There is a y on the top and the bottom of the fraction. Recall that when dividing the same number raised to exponents, we subtract the exponents.

3 * x^5 * y^2   or    3x^5y^2
2 * z^3                      2z^3

There is nothing else we can simplify, so that is the simplest form of the expression.