simplify solutions

Question

Struggling with a few of my homework. Just dont understand how to solve them. Please tell me the rules. My teacher goes way too fast and I'm confused. Thanks

 

X⁸y³

------

X³y³

 

 

 

 

 

X⁸y⁴

---------

Xyz

 

 

 

 

15x⁶

--------

5x⁶

 

 

 

 

A⁵b⁶

--------

A³b¹

Answer 1

The answer to the third problem is 3, not 5.

 

15x^6 / 5x^6 = 3 since x^6/x^6 = 1 and 15/5 = 3. 3 * 1 = 3.

Answer 2

Hi Jackson, work this type of problem in parts. Start with the coefficients, then take each variable separately.

 

Remember the rules for exponents:

 

aⁿ * a^m = a^n+m

 

aⁿ / a^m = a^n-m

 

a⁰ = 1

 

First example:

 

x⁸y³ / x³y³

 

Both the numerator and denominator have coefficients of 1, therefore nothing needs to be done with them.

 

x variable:

 

x⁸ / x³ = x^8-3 = x⁵

 

y variable:

 

y³ / y³ = y^3-3 = y⁰ = 1

 

Now put the parts back together:

 

There are no coefficients to worry about and the y terms cancel out leaving only the x term:

 

Answer: x⁵

 

Third example:

 

Part 1, the coefficients:

 

15 / 3 = 5

 

x variable:

 

x⁶ / x⁶ = x^6-6 = x⁰ = 1

 

Put the parts back together, noting the x terms cancel out leaving only the coefficients.

 

Answer: 5

 

Questions?