Question

Simplify: 10x^4y^2x^3y^6


A. 10x^7y^8

B. (10xy)^15

C. 10x^6y^9

D. 10x^12y^12

Answer 1

Consider the following:
\[x^2x^3\]So how do we combine these? What's the rule? do we add or multiply the exponents?

Take a second to examine it, and you'll realize, hey, this isn't so bad:
\[x^2=x*x\]\[x^3=x*x*x\]so simply,\[x^2x^3=x*x*x*x*x\]That's just 5 x's multiplied by each other, so knowing that, you know can just add exponents together when you have the same term with different exponents multiplied by each other.

If you ever forget, just expand it out like I did to check for yourself.

Answer 2

A.