Question

What is the solution to question 5) a. and 5) b.

Answer 1

`a.\\3(x^2)^6(2x^3)^4=3x^(2\cdot6)(2^4)(x^3)^4=3x^(12)(16)(x^(3\cdot4))\\\\=48x^(12)x^(12)=48x^(12+12)=48x^(24)\\\\\text{Used:}\\(a^n)^m=a^(nm)\\\\(ab)^n=a^nb^n`

`b.\\5x^(5n)\cdot(-3x^2)=-(5\cdot3)x^(5n)x^2=-15x^(5n+2)\\\\\text{Used:}\\\\a^n\cdot a^m=a^(n+m)`

`c.\\(100b^(2n))/(-20b^5)=(100)/(-20)b^(2n-5)=-5b^(2n-5)\\\\\text{Used:}\\\\(a^n)/(a^m)=a^(n-m)`