Question

Please help me with this Algebra I question.

Answer 1

`-(b^2)/(16a^4)`

Explanation:

Given expression:

`((2a)^(-2)b^5)/(-4a^2b^3)`

`\textsf{Apply the exponent rule}\quad (ab)^c=a^c \cdot b^c:`

`\implies (2^(-2)a^(-2)b^5)/(-4a^2b^3)`

Separate the variables:

`\implies (2^(-2))/(-4)\cdot (a^(-2))/(a^2)\cdot (b^5)/(b^3)`

`\textsf{Apply the exponent rule} \quad (a^b)/(a^c)=a^(b-c):`

`\implies (2^(-2))/(-4)\cdot a^(-2-2)\cdot b^(5-3)`

`\implies (2^(-2))/(-4)\cdot a^(-4)\cdot b^(2)`

`\textsf{Apply the exponent rule}\quad a^(-n)=(1)/(a^n):`

`\implies (1)/(-4(2^2))\cdot (1)/(a^4)\cdot b^(2)`

`\implies -(1)/(16)\cdot (1)/(a^4)\cdot b^(2)`

Simplify:

`\implies -(b^2)/(16a^4)`