rule
For all numbers x and y and integers n,
quotxy
Gal3


BOTH the "top" and the "bottom" get raised to the new power!

When a quotient is raised to a power, the numerator will be raised to the power, AND the denominator will be raised to the power.

When in doubt, expand terms to see what is happening.

quotpic
quotex

This expanded version shows how each factor of the quotient is raised to the new power.quot11

Consider this interpretation using a negative exponent in the quotient.xdiv

Examples: (numerical and algebraic applications)

1. qt1 
Notice that the exponent is applied to both the numerator and the denominator.		 2. qex1
This problem also involves using the "power to a power" rule for (a2)3 = a6.

3.  qt3
When working with a negative exponent, you can apply the exponent step-by-step, as shown here.
Remember that an answer does not contain a complex fraction (a fraction over another fraction).
4. Applying a negative exponent in a step-by-step process.
qt4Did you notice in this problem that raising a fraction to a negative one power, flipped the fraction over?

 5. Applying a negative exponent by remembering that the negative exponent means the term in on the wrong side of the fraction bar.
exq3
6. rm33
Notice how the negative sign is being handled with the product in the numerator. Each term of the product is raised to -3 power.		 7. exq4
A negative power raised to a negative power is a positive power. Again, notice how the numerator product is being handled.

 

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