Chapter 5: Q62. (page 227)

Prove the Power of a Product Property, ${(a b)}^{m} = a^{m} b^{m}$ .

Short Answer

Expert verified

It is proved that ${(a b)}^{m} = a^{m} b^{m}$ .

Step by step solution

Step 1. Given Information.

Given to prove the Power of a Product Property ${(a b)}^{m} = a^{m} b^{m}$ .

Step 2. Explanation.

Rewriting the given expression:

$\begin{array}{l} {(a b)}^{m} = a b \times a b \times a b \times ... mtimes \\ {(a b)}^{m} = a \times b \times a \times b \times a \times b \times ... mtimes \\ {(a b)}^{m} = (a \times a \times a ... mtimes) \times (b \times b \times b \times ... mtimes) \\ {(a b)}^{m} = a^{m} b^{m} \end{array}$

Step 3. Conclusion.

Hence, It is proved that ${(a b)}^{m} = a^{m} b^{m}$ .

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Prove the Power of a Product Property, ${(a b)}^{m} = a^{m} b^{m}$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explanation.

Step 3. Conclusion.

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Prove the Power of a Product Property, ${(a b)}^{m} = a^{m} b^{m}$ .