Can someone please tell me how to solve problems like: x^2y^8*x^3y^(-13)/xy^3 ?

Question

x²y⁸ * x³y^(-13)/xy³

If someone answers, can you please thoroughly explain how you got the answer and how to do it? I tried calculating questions like this on different websites, but, since I have never been told how to do it and am only in middle school, their explanations confuse me. I'd really appreciate the help! Thank you in advance.

Answer 1

x ² y ⁸ * x ³ y^(-13)/x y ³

numerator =x ² y ⁸ * x ³ y^(-13)

denominator = x y ³

first we will simplify numerator using law of exponent

x ² y ⁸ * x ³ y^(-13)

= x ² y ⁸ x ³ y^-13

= x ² x ³ y ⁸ y ^-13

= x ²⁺³ y ^{8+ (-13)} ........... law of exponent multiplication rule ( a ^m * a ⁿ = a ^m+n )

= x ⁵ y ^-5

so

numerator= x ⁵ y ^-5

denominator = x y ³

numerator / denominator

= x ⁵ y ^-5 / x y ³

Now we will use Law of exponent division rule a^m / a ⁿ = a ^m-n

= x ^{5 -1} y ^{-5 -3}

= x ⁴ y ^-8

= x ⁴ / y ⁸ ............. law of exponent : negative exponent ( a ^-m = 1/ a ^m )