Question

Explain how to use properties of powers to simplify the expression 27 . 3^2.

Answer 1

We can use the product of powers property to solve the exercise.

`a^m\cdot a^n=a^(m+n)`

We can rewrite 27 like this:

`27=3\cdot3\cdot3=3^3`

Now, we can apply the property:

`\begin{gathered} 27\cdot3^2=3^3\cdot3^2 \\ 27\cdot3^2=3^(3+2) \\ 27\cdot3^2=3^5 \\ 27\cdot3^2=3\cdot3\cdot3\cdot3\cdot3 \\ 27\cdot3^2=243 \end{gathered}`

Therefore, the result of simplifying the expression is 243.