Question

which shows the power rule used correctly? $(ab)^5$

Explanation:

Step1: Recall the Power Rule for Products

The Power Rule for a product \((xy)^n\) states that \((xy)^n = x^n y^n\). This means we raise each factor in the product to the given power.

Step2: Apply the Rule to \((ab)^5\)

Using the Power Rule for Products, we raise \(a\) to the power of \(5\) and \(b\) to the power of \(5\). So, \((ab)^5 = a^5b^5\).

Step3: Compare with the Options

• First option: \(ab^5\) – only \(b\) is raised to the 5th power, incorrect.
• Second option: \(a^6b^6\) – the exponent is 6 instead of 5, incorrect.
• Third option: \(a^5b\) – only \(a\) is raised to the 5th power, incorrect.
• Fourth option: \(a^5b^5\) – matches the result from the Power Rule, correct.

Answer:

The correct option is the fourth one, which is \(a^5b^5\) (the rightmost option among the four given). If we consider the options as labeled (assuming from left to right as Option 1, Option 2, Option 3, Option 4), then the answer is Option 4: \(a^5b^5\)