Question

When a product is raised to a power, it is equal to the product of each factor raised to that power. Show that this rule does not apply for a sum or difference to a power using the problem (5 – 3)². You may indicate an exponent in your answer with ^. For example, 3x² as 3x^2.

Answer 1

This problem is asking you to make a mistake when using power rules. It wants you to first calculate

\[(5-3)^2 = (2)^2 = 4\]
and then incorrectly use the power rule described for a product of powers, raised to a power.

That is, this problem is asking you to purposely make the mistake of doing this:

\[(5-3)^2 = (5^2 - 3^2) = (25 - 9) = 16\]

Clearly, you can see that 16 does not equal 4, so that was the incorrect way to work this problem.

Answer 2

thank u!!

Answer 3

You're welcome!