Question

Simplify the following expression by using the exponential laws \(\frac{(x^2y)^3}{xy}\)

Answer 1

Using the exponential laws, we can simplify the numerator as follows:$$(x^2y)^3 = x^{2\cdot 3}y^3 = x^6y^3$$So the expression becomes:$$\frac{x^6y^3}{xy}$$Now we can simplify the denominator by writing $xy = x^1y^1$, so:$$\frac{x^6y^3}{x^1y^1}$$Finally, we can apply the division law of exponents, which states that $x^a\div x^b = x^{a-b}$, to get:$$x^{6-1}y^{3-1} = x^5y^2$$Therefore, the simplified expression is $x^5y^2$.