Question

Which expression is equivalent to ((2a^-3 b^4)^2/(3a^5 b) ^-2)^-1

Answer 1

1 / 36a^4 b^10

Explanation:

Answer 2

`\large\boxed{(1)/(36a^4b^(10))}`

Explanation:

`\left((\left(2a^(-3)b^4\right)^2)/(\left(3a^5b\right)^(-2))\right)^(-1)\qquad\text{use}\ a^(-1)=(1)/(a)\\\\=(\left(3a^5b\right)^(-2))/(\left(2a^(-3)b^4\right)^2)\qquad\text{use}\ (ab)^n=a^nb^n\\\\=(3^(-2)(a^5)^(-2)b^(-2))/(2^2(a^(-3))^2(b^4)^2)\qquad\text{use}\ (a^n)^m=a^(nm)\\\\=(3^(-2)a^((5)(-2))b^(-2))/(4a^((-3)(2))b^((4)(2)))=(3^(-2)a^(-10)b^(-2))/(4a^(-6)b^8)\qquad\text{use}\ (a^n)/(a^m)=a^(n-m)`

`=(3^(-2))/(4)a^(-10-(-6))b^(-2-8)=(3^(-2))/(4)a^(-4)b^(-10)\qquad\text{use}\ a^(-n)=(1)/(a^n)\\\\=(1)/(3^2)\cdot(1)/(4)\cdot(1)/(a^4)\cdot(1)/(b^(10))=(1)/(36a^4b^(10))`