Question

2) Simplify and solve the following polynomials. Show your solution.a) (3z^8)^15 + (m^12)^6

Answer 1

Lets start by copying the polynomial:

`(3x^8)^(15)+(m^(12))^6`

To simplify, we will need to use the following properties:

`\begin{gathered} \mleft(a^cb^d\mright)^f=a^(cf)b^(df) \\ \mleft(a^b\mright)^c=a^(bc) \end{gathered}`

We will apply the first property to the first term and the second property to the second term:

`\begin{gathered} (3x^8)^(15)+(m^(12))^6= \\ =3^(1\cdot15)x^(8\cdot15)+m^(12\cdot6)= \\ =3^(15)x^(120)+m^(72) \end{gathered}`

So, the simplification is:

`(3x^8)^(15)+(m^(12))^6=3^(15)x^(120)+m^(72)`