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.