Question

((4x^5y)/(16xy^4))^3 Solve and Explain.

Answer 1

The given question is indices. we will be using laws of indices to solve it. This are some of the laws;

`\begin{gathered} a^m* a^n=^{}a^(m+n) \\ (a^m)/(a^n)=a^(m-n) \\ (a^m)^n=a^(mn) \end{gathered}`

Given the expression;

`((4x^5y)/(16xy^4))^3`

Simplify using the laws as shown;

`\begin{gathered} =((4)/(16)*(x^5)/(x)*(y)/(y^4))^3 \\ =((1)/(4)^{}x^(5-1)y^(1-4))\text{ }^3 \\ =((1)/(4)^{}x^4y^(-3))\text{ }^3 \\ =\text{ }((1)/(4)^{})^3(x^4)^3(y^(-3))\text{ }^3 \\ =\text{ }(1)/(64)x^(12)y^(-9) \end{gathered}`

Hence the simplified form of the expression is;

`(1)/(64)x^(12)y^(-9)`