## Example Questions

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### Example Question #40 : Complex Numbers

Raise to the fourth power. None of these    Explanation:

By the Power of a Power Rule, the fourth power of any number is equal to the square of the square of that number: Therefore, one way to raise to the fourth power is to square it, then to square the result.

Using the binomial square pattern to square : Applying the Power of a Product Property: Since by definition:   Square this using the same steps:     ### Example Question #51 : Squaring / Square Roots / Radicals

Raise to the fourth power.

None of these     Explanation:

The easiest way to find is to note that .

Therefore, we can find the fourth power of by squaring , then squaring the result.

Using the binomial square pattern to square : Applying the Power of a Product Property: Since by definition:   Square this using the same steps:     Therefore, ### Example Question #41 : Complex Numbers

Raise to the third power.

None of these     Explanation:

To raise any expression to the third power, use the pattern Setting : Taking advantage of the Power of a Product Rule: Since and :  Collecting real and imaginary terms:  ### Example Question #51 : Squaring / Square Roots / Radicals

Evaluate:   The expression is undefined   Explanation: is defined to be equal to for any real or imaginary and for any real ; therefore, To evaluate a positive power of , divide the power by 4 and note the remainder: Therefore, Substituting, Rationalizing the denominator by multiplying both numerator and denominator by : 1 3 Next →

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