Question

How do you solve this rational exponent (25b^6)^-1.5?

Answer 1

`Use:\left(a^n\right)^m=a^(n\cdot m)\ and\ (a\cdot b)^n=a^n\cdot b^n\\\\25=5^2\\\\(25b^6)^(-1.5)=\left(5^2b^6\right)^(1.5)=\left(5^2\right)^(-1.5)\cdot\left(b^6\right)^(-1.5)=5^(2\cdot(-1.5))\cdot b^(6\cdot(-1.5))\\\\=5^(-3)b^(-9)=(1)/(5^3b^9)=\boxed{(1)/(125b^9)}`