Question

Simplify by writing the expression with positive exponents. Assume that all variables represent nonzero real numbers

Answer 1

`\lbrack(144q^2)/(m^6p^4)\rbrack^{}`

Step-by-step explanation

Let's remember some properties ofthe fractions ans exponents,

`\begin{gathered} a^(-n)=(1)/(a^n) \\ ((a)/(b))^n=(a^n)/(b^n) \\ (ab)^n=a^nb^n \\ (a^n)^m=a^(m\cdot n) \end{gathered}`

so

Step 1

`\lbrack(4p^(-2)q)/(3^(-1)m^3)\rbrack^2`

reduce by using the properties

`\begin{gathered} \lbrack(4p^(-2)q)/(3^(-1)m^3)\rbrack^2 \\ \lbrack(4q)/(3^(-1)m^3p^2)\rbrack^2 \\ \lbrack(3^1\cdot4q)/(m^3p^2)\rbrack^2 \\ \lbrack(12q)/(m^3p^2)\rbrack^2 \\ \lbrack(144q^2)/(m^(3\cdot2)p^(2\cdot2))\rbrack^{} \\ \lbrack(144q^2)/(m^6p^4)\rbrack^{} \end{gathered}`

therefore, the answer is

`\lbrack(144q^2)/(m^6p^4)\rbrack^{}`

I hope this helps you