Q1. - Algebra 2

Question

Write an example that illustrates a property of powers. Then use multiplication or division to explain why it is true.

Step-by-Step Solution

Answer

The example for product of powers is $2^3\cdot 2^4=2^7$ .

Step 1. Given Information.

Given to write an example that illustrates a property of powers and then to use multiplication or division to explain why it is true. 

Step 2. Explanation .

Considering the product of powers:

Let the example be  $2^3\cdot 2^4=2^7$

 

According the product of powers i.e.$a^m\cdot a^n=a^{m+n}$  , the example can be proven as below:

 $\begin{array}{l}{2}^3\cdot 2^4=2^{3+4}\\ 2^3\cdot 2^4=2^7\end{array}$

 Checking the rule using multiplication:

$\begin{array}{l}{2}^3\cdot 2^4=(2\cdot 2\cdot 2)\cdot (2\cdot 2\cdot 2\cdot 2)\\ 2^3\cdot 2^4=2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\\ 2^3\cdot 2^4=2^7\end{array}$ 

Step 3. Conclusion .

Hence, the product of powers is always true.