Question

Tyrone claims that the first step to simplify this expression is to raise the numerator and denominator to the third power. Alisha claims that the first step to simplify is to apply the quotient of powers. Who is correct? Explain.

(StartFraction m squared n Superscript negative 3 Baseline Over m Superscript 6 Baseline n Superscript negative 1 Baseline EndFraction) cubed
Sample Response: Both are correct. Either rule applied first will have the same result. Both rules will be used either way, and the order in which they are applied does not matter as long as they are applied correctly at each step.

Which did you include in your response?
Both are correct.
Order does not matter.
The results are the same whatever the order.
Be sure to apply the rules properly.

Answer 1

Both Tyrone and Alisha are correct about simplifying the expression with exponents: the order of applying the exponent rules does not affect the final result. Both the quotient of powers rule and raising the entire fraction to a power will be used to simplify the given expression, and applying either step first will yield the same simplified form.

Step-by-step explanation:

In mathematics, the correct approach to simplify an expression like (m2n-3 / m6n-1)3 involves understanding the rules of exponents. Both Tyrone and Alisha are correct in this case. Applying the quotient of powers means you subtract the exponents when dividing like bases, and raising the entire fraction to the third power means applying the power to each term inside.

To simplify this, one can follow either approach because the order in which these operations are applied does not affect the final result. One approach is to first apply the quotient rule (subtract exponents) and then raise to the third power, or vice versa.

Here's the step-by-step explanation:

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Alternatively, you could:

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