Question

Division Properties of Exponents HWQuestion: Simplify the following expressions.

Answer 1

`(x^3)/(y^9)`

Step-by-step explanation:

To simplify the expression, we will use the following properties:

`\begin{gathered} (x^a)^b_{}=x^(a\cdot b) \\ (x^a)/(x^b)=x^(a-b) \end{gathered}`

Therefore, first, apply the exponent to the numerator and the denominator of the fraction:

`((x^2)/(xy^3))^3=((x^2)^3)/((xy^3)^3)`

Then, using the first property, we get:

`((x^2)^3)/(x^3(y^3)^3)=(x^(2\cdot3))/(x^3y^(3\cdot3))=(x^6)/(x^3y^9)`

Finally, use the second property:

`(x^6)/(x^3)\cdot(1)/(y^9)=x^(6-3)\cdot(1)/(y^9)=x^3\cdot(1)/(y^9)=(x^3)/(y^9)`

Therefore, the simplified expression is:

`\frac{x^3^{}}{y^9}`