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

Explain how to use properties of powers to simplify the expression 27 . 3^2.-example-1

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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.

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