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Chapter 5: Q1. (page 226)

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

Short Answer

Expert verified

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

Step by step solution

01

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.

02

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:

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

03

Step 3. Conclusion.

Hence, the product of powers is always true.

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