Question

Rewrite each expression as a product of two powers or a quotient of two powers3^10(32^5*3)^2

Answer 1

`3^(10)(32^5\cdot3)^2`

Distributing the exponent:

`\begin{gathered} 3^(10)\lbrack(32^5)^2\cdot3^2\rbrack= \\ =3^(10)(32^(5\cdot2)\cdot3^2)= \\ =3^(10)(32^(10)\cdot3^2) \end{gathered}`

Applying commutative property:

`\begin{gathered} 3^(10)\cdot3^2\cdot32^(10)= \\ =3^(10+2)\cdot32^(10)= \\ =3^(12)\cdot32^(10) \end{gathered}`