Question

(x^3y^5)^3 × -x^6y^5

Answer 1

To simplify the expression you can first use this property of exponents

`(a\cdot b)^m=a^mb^m`

Then you have

`\begin{gathered} (x^3y^5)^3=(x^3)^3(y^5)^3 \\ (x^3y^5)^3=x^(3\cdot3)y^(5\cdot3) \\ (x^3y^5)^3=x^9y^(15) \end{gathered}`

Now apply this property of exponents

`a^b\cdot a^c=a^(b+c)`

Therefore, you have

`\begin{gathered} (x^3y^5)^3\cdot-x^6y^5=x^9y^(15)\cdot-x^6y^5 \\ (x^3y^5)^3\cdot-x^6y^5=x^9\cdot-x^6\cdot y^(15)\cdot y^5 \\ (x^3y^5)^3\cdot-x^6y^5=-x^(9+6)\cdot y^(15+5) \\ (x^3y^5)^3\cdot-x^6y^5=-x^(15)\cdot y^(20) \\ (x^3y^5)^3\cdot-x^6y^5=-x^(15)y^(20) \end{gathered}`