I don't know what you mean by "power of product law" or "power of a quotient law". I have never heard of those "laws". If you mean just combining the two laws then you might consider using fractional powers.
Hey guys,
the task: Create four expressions that, when simplified using the exponent laws, are equal to 4x^6.
1. Product Law = (4x^2) (x^4) = 4x^6
2. Quotient Law =
16x^8

4x^2
= 4x^6
3. Power of a Power Law = (2x^3)^2 = 4x^6
Is there any chance to create an expression for 4x^6 with the Power of Product Law or Power of a Quotient Law?
That is in my grade 10 math book.
Power of a Product Law = When the base is a product, apply the exponent to each factor in the base. (xy)^m = x^m y^m
Power of a Quotient Law = When the base is a quotient, apply the exponent to the numerator and denominator.
x ^m

y
x and y are together in brackets.
=
x^m

y^m
Thats what I got here.