Question

Which expression is equivalent to -3a^-2b^3/15a^-7b^-1

Answer 1

`\large\boxed{(-3a^(-2)b^3)/(15a^(-7)b^(-1))=-(1)/(5)a^5b^4=-(a^5b^4)/(5)}`

Explanation:

`(-3a^(-2)b^3)/(15a^(-7)b^(-1))=(-3)/(15)\cdot (a^(-2))/(a^(-7))\cdot(b^3)/(b^(-1))\qquad\text{use}\ (x^n)/(x^m)=x^(n-m)\\\\=-(3\!\!\!\!\diagup^1)/(15\!\!\!\!\!\diagup_5)\cdot a^(-2-(-7))\cdot b^(3-(-1))=-(1)/(5)a^(-2+7)b^(3+1)=-(1)/(5)a^5b^4`