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We begin by using the power rule for parentheses.
That is, the power applied to a product inside parentheses is applied to each of the terms within when the parentheses are opened,
We apply the above rule to the given problem:
Therefore, the correct answer is option d.
Note:
According to the formula of the power property inside parentheses mentioned above, it might seem as though it refers to only two terms of the product inside of the parentheses, but in reality, it is also valid for the power over a multiplication of many terms inside parentheses, as was seen above.
A good exercise is to demonstrate that if the previous property is valid for a power over a product of two terms inside parentheses (as formulated above), then it is also valid for a power over several terms of the product inside parentheses (for example - three terms, etc.).
\( 112^0=\text{?} \)
Because of the power rule for products! When you have , it equals . The exponent must be applied to every factor inside the parentheses.
That would give you , which is mathematically correct but much harder to work with! The distributed form is the simplified answer they want.
Absolutely! The power rule works for any exponent. For example: . Negative exponents follow the exact same pattern.
Look for the option where every single factor has the same exponent as the original power. In this case, all four numbers (3, 2, 4, 6) should have the -4 exponent.
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