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:

$\begin{gathered} 3^{10}\cdot3^2\cdot32^{10}= \\ =3^{10+2}\cdot32^{10}= \\ =3^{12}\cdot32^{10} \end{gathered}$