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

the first statement
**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.
**
means, for example
\[ (3 \cdot 5)^2 = 3^2 \cdot 5^2 \]
as a check, note that 3*5= 15
\[ 15^2= 225 \]
also,
\[3^2 * 5^2 = 9 * 25= 225 \]
it works!

Answer 2

they want you to show
**Show that this rule does not apply for a sum or difference to a power **
does not work.

in other words
\[ (5-3)^2 ≠ 5^2 - 3^2 \]
that is not hard to do. simplify both sides, and show they are not the same number