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Chapter 2: Problem 5

If \(a \neq 0\) and \(b \neq 0\), show that \(1 /(a b)=(1 / a)(1 / b)\).

Short Answer

Expert verified
The proved statement according to this solution is that \(1 /(a b)=(1 / a)(1 / b)\) for all \(a \neq 0\) and \(b \neq 0\)

Step by step solution

01

Write the original equality

Start by writing the given equation which needs to be proved. The equation is \(1 /(a b)=(1 / a)(1 / b)\)
02

Apply the reciprocal rule

The reciprocal rule states that the reciprocal of a product of two numbers is equal to the product of the reciprocals of the two numbers. So, we can write the left hand side as \((1 / a)(1 / b)\)
03

Validate the equality

Now, the left side of the equation will look exactly the same as the right side of the equation. Therefore, we have proved that \(1 /(a b)=(1 / a)(1 / b)\) for all \(a \neq 0\) and \(b \neq 0\)

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If \(0
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